Results in Applied Mathematics最新文献

{"title":"Schistosomiasis mathematical model in a spatially heterogeneous environment","authors":"Franck Eric Thepi Nkuimeni ,&nbsp;Berge Tsanou","doi":"10.1016/j.rinam.2024.100488","DOIUrl":"10.1016/j.rinam.2024.100488","url":null,"abstract":"<div><p>Schistosomiasis is classified by WHO as a neglected tropical disease. Recent research works have shown that large-scale development projects involving massive population displacement and water irrigation, such as the construction of dams, lakes, and the development of agricultural areas, favour the proliferation of bilharzia. These observations motivate us to propose a reaction–diffusion model to assess the role of the displacements of humans, snails, cercaria, miracidia in the transmission dynamics of Schistosomiasis. The model incorporates a general non-linear contact functions and density-dependent parameters. The aim is to better understanding the role of spatial interactions on the spread of Schistosomiasis, in order to propose appropriate recommendations for the control of that silent threat. We characterize the basic reproduction number <span><math><msub><mrow><mi>R</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> of the model. The uniform persistence theory, the maximum principle are used to conduct an in-depth analysis of both the homogeneous and heterogeneous models. Theoretical results are illustrated through numerical simulations.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100488"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259003742400058X/pdfft?md5=e857e903b9525a96f507d65c9af41c26&pid=1-s2.0-S259003742400058X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142011276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical approximation of Volterra integral equations with highly oscillatory kernels","authors":"Suliman Khan","doi":"10.1016/j.rinam.2024.100483","DOIUrl":"10.1016/j.rinam.2024.100483","url":null,"abstract":"<div><p>The Volterra integral equations (VIEs) with oscillatory kernels arise in several applied problems and need to be treated with a computational method have multiple characteristics. In the literature (Zaheer-ud-Din et al., 2022; Li et al., 2012), the Levin method combined with multiquadric radial basis functions (MQ-RBFs) and Chebyshev polynomials are well-known techniques for treating oscillatory integrals and integral equations with oscillatory kernels. The numerical experiments show that the Levin method with MQ-RBFs and Chebyshev polynomials produces dense and ill-conditioned matrices, specifically in the case of large data and high frequency. Therefore, the main task in this study is to combine the Levin method with compactly supported radial basis functions (CS-RBFs), which produce sparse and well-conditioned matrices, and subsequently obtain a stable, efficient, and accurate algorithm to treat VIEs. The theoretical error bounds of the method are derived and verified numerically. Although the error bounds obtained are not improved significantly, alternatively, a stable and efficient algorithm is obtained. Several numerical experiments are performed to validate the capabilities of the proposed method and compare it with counterpart methods (Zaheer-ud-Din et al., 2022; Li et al., 2012).</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100483"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000530/pdfft?md5=86d1f891aabdcd5eb5d45ac6c28ff264&pid=1-s2.0-S2590037424000530-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141961273","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Smooth transition and Gibbs oscillation minimization in a 7-point subdivision scheme with shape-control parameters for high smoothness","authors":"Rabia Hameed ,&nbsp;Ghulam Mustafa ,&nbsp;Tayyabah Latif ,&nbsp;Samsul Ariffin Abdul Karim","doi":"10.1016/j.rinam.2024.100485","DOIUrl":"10.1016/j.rinam.2024.100485","url":null,"abstract":"<div><p>Computer graphics is a dynamic field that heavily relies on mathematical techniques. For instance, subdivision scheme is used to create smooth and visually appealing curves and surfaces of arbitrary topology. The primary focus of this study is to transform two 5-point binary subdivision schemes into a single 7-point binary subdivision scheme with shape control. We have merged two binary approximating schemes that were constructed using the uniform B-spline basis function and the Lagrange basis function into a new subdivision scheme. It has been demonstrated that, for fixed values of the global shape control parameters, the curves generated by the proposed 7-point binary subdivision scheme maintain <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span> continuity everywhere. Furthermore, a brief discussion on the analysis of the Gibbs phenomenon in the new subdivision scheme has been presented. This is also a reminder of the challenges and intricacies involved in computer graphics and geometric modeling.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100485"},"PeriodicalIF":1.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000554/pdfft?md5=4803d54ddef3cb635f80256af567821a&pid=1-s2.0-S2590037424000554-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141985082","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical analysis of the stochastic FitzHugh–Nagumo model driven by multiplicative noise based on the spectral Galerkin method","authors":"Rushuang Yang ,&nbsp;Huanrong Li","doi":"10.1016/j.rinam.2024.100477","DOIUrl":"10.1016/j.rinam.2024.100477","url":null,"abstract":"<div><p>The stochastic FitzHugh–Nagumo (FHN) neural information transduction model has been widely used in different fields, but there are few numerical studies on this model. In this paper, the stochastic FHN model driven by multiplicative noise is studied based on the spectral Galerkin method. The model is firstly discreted by semi-implicit Euler–Maruyama scheme in time and spectral Galerkin method in space. The error estimation and convergence order are then analyzed. Finally, the one-dimensional and two-dimensional stochastic FHN models are numerically calculated and the convergence order is verified. Moreover, this study promotes the understanding of the information transmission law of neural information transmission model under the influence of stochastic factors.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100477"},"PeriodicalIF":1.4,"publicationDate":"2024-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000475/pdfft?md5=953719a9089f7a91744ddf3bfd2f302c&pid=1-s2.0-S2590037424000475-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736792","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence and general decay for a nonlinear wave equation with acoustic and fractional boundary conditions coupling by source and delay terms","authors":"Abdelbaki Choucha ,&nbsp;Salah Boulaaras ,&nbsp;Behzad Djafari-Rouhani ,&nbsp;Rafik Guefaifia ,&nbsp;Asma Alharbi","doi":"10.1016/j.rinam.2024.100476","DOIUrl":"10.1016/j.rinam.2024.100476","url":null,"abstract":"<div><p>This work deal with global existence and general decay of solutions of a wave equation with acoustic and fractional boundary conditions coupling by source and delay terms. Under some hypotheses, we study the global existence of the solution and by suitable Lyapunov function the general decay result is proved.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100476"},"PeriodicalIF":1.4,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000463/pdfft?md5=3fa82e2c38a50e43a044f945f8b298a1&pid=1-s2.0-S2590037424000463-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141623026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On shape and topological optimization problems with constraints Helmholtz equation and spectral problems","authors":"Mame Gor Ngom ,&nbsp;Ibrahima Faye ,&nbsp;Diaraf Seck","doi":"10.1016/j.rinam.2024.100474","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100474","url":null,"abstract":"<div><p>Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modelled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal shapes obstacles to mitigate sand transport under the constraint of the Helmholtz equation. And the second side of this work is related to Dirichlet and Neumann spectral problems. We show the existence of optimal shapes in a general admissible set of quasi open sets. And necessary optimality conditions of first order are given in a regular framework using both shape and topological optimization. Some numerical simulations are given to represent optimal domains.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100474"},"PeriodicalIF":1.4,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259003742400044X/pdfft?md5=1bac6e4d175ca7207d9cd34940f1cd45&pid=1-s2.0-S259003742400044X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141607666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A general law of the iterated logarithm for non-additive probabilities","authors":"Zhaojun Zong ,&nbsp;Miaomiao Gao ,&nbsp;Feng Hu","doi":"10.1016/j.rinam.2024.100475","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100475","url":null,"abstract":"<div><p>Motivated by some interesting problems in mathematical economics, quantum mechanics and finance, non-additive probabilities have been used to describe the phenomena which are generally non-additive. In this paper, we further study the law of the iterated logarithm (LIL) for non-additive probabilities, based on existing results. Under the framework of sublinear expectation initiated by Peng, we give two convergence results of <span><math><mrow><msub><mrow><mi>V</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>≔</mo><mfrac><mrow><msubsup><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>n</mi></mrow></msubsup><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub></mrow><mrow><msqrt><mrow><mi>n</mi></mrow></msqrt><mi>ϕ</mi><mrow><mo>(</mo><mi>n</mi><mo>)</mo></mrow></mrow></mfrac></mrow></math></span> under some reasonable assumptions, where <span><math><msubsup><mrow><mrow><mo>{</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>}</mo></mrow></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></math></span> is a sequence of random variables and <span><math><mi>ϕ</mi></math></span> is a positive nondecreasing function. From these, a general LIL for non-additive probabilities is proved for negatively dependent and non-identically distributed random variables. It turns out that our result is a natural extension of the Kolmogorov LIL and the Hartman–Wintner LIL. Theorem 1 and Theorem 2 in this paper can be seen an extension of Theorem 1 in Chen and Hu (2014).</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100475"},"PeriodicalIF":1.4,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000451/pdfft?md5=fc6eb3a1286d72ec3562e2dc6bd8f382&pid=1-s2.0-S2590037424000451-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141607665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Oscillatory properties for Emden–Fowler type difference equations with oscillating coefficients","authors":"Yaşar Bolat ,&nbsp;Murat Gevgeşoğlu ,&nbsp;George E. Chatzarakis","doi":"10.1016/j.rinam.2024.100472","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100472","url":null,"abstract":"<div><p>In this paper, we give new criteria on the oscillation of the fourth-order Emden–Fowler type delay difference equation with oscillating coefficients of the form <span><span><span><math><mrow><mi>Δ</mi><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>r</mi></mrow><mrow><mi>n</mi></mrow></msub><msubsup><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>τ</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mo>=</mo><mn>0</mn><mtext>,</mtext><mi>n</mi><mo>≥</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>0</mn></mrow></msub><mtext>,</mtext></mrow></math></span></span></span>where <span><math><mrow><msub><mrow><mi>W</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>p</mi></mrow><mrow><mi>n</mi></mrow></msub><msup><mrow><mfenced><mrow><msup><mrow><mi>Δ</mi></mrow><mrow><mn>3</mn></mrow></msup><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi>α</mi></mrow></msup></mrow></math></span> and <span><math><mrow><msub><mrow><mi>v</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>=</mo><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi></mrow></msub><mo>+</mo><msub><mrow><mi>q</mi></mrow><mrow><mi>n</mi></mrow></msub><msub><mrow><mi>y</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>σ</mi></mrow></msub></mrow></math></span>. For this we use the Riccati transformation method and the comparison method. Also we give some examples to illustrate our results.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100472"},"PeriodicalIF":1.4,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000426/pdfft?md5=a75c766551a918235e26d7441f4c4d69&pid=1-s2.0-S2590037424000426-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542779","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Boundedness and asymptotic behavior in a quasilinear chemotaxis system with nonlinear diffusion and singular sensitivity for alopecia areata","authors":"Luxu Zhou,&nbsp;Fugeng Zeng,&nbsp;Lei Huang","doi":"10.1016/j.rinam.2024.100473","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100473","url":null,"abstract":"&lt;div&gt;&lt;p&gt;This paper is concerned with a three-component quasilinear chemotaxis system with nonlinear diffusion and singular sensitivity for alopecia areata &lt;span&gt;&lt;span&gt;&lt;span&gt;&lt;math&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;χ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mfenced&gt;&lt;mrow&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;∇&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;μ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;γ&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/msup&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Δ&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;/mtd&gt;&lt;mtd&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;x&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;∈&lt;/mo&gt;&lt;mi&gt;Ω&lt;/mi&gt;&lt;mo&gt;×&lt;/mo&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;v&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;ν&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfrac&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfrac&gt;&lt;mrow&gt;&lt;mi&gt;∂&lt;/mi&gt;&lt;mi&gt;w&lt;/mi&gt;&lt;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in Applied Mathematics","volume":"23 ","pages":"Article 100473"},"PeriodicalIF":1.4,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000438/pdfft?md5=1c7b136d913734673823e8437fc9fa7f&pid=1-s2.0-S2590037424000438-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141542698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Propagation reversal on trees in the large diffusion regime","authors":"Hermen Jan Hupkes ,&nbsp;Mia Jukić","doi":"10.1016/j.rinam.2024.100468","DOIUrl":"https://doi.org/10.1016/j.rinam.2024.100468","url":null,"abstract":"<div><p>In this work we study travelling wave solutions to bistable reaction–diffusion equations on bi-infinite <span><math><mi>k</mi></math></span>-ary trees in the continuum regime where the diffusion parameter is large. Adapting the spectral convergence method developed by Bates and his coworkers, we find an asymptotic prediction for the speed of travelling front solutions. In addition, we prove that the associated profiles converge to the solutions of a suitable limiting reaction–diffusion PDE. Finally, for the standard cubic nonlinearity we provide explicit formulas to bound the thin region in parameter space where the propagation direction undergoes a reversal.</p></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"23 ","pages":"Article 100468"},"PeriodicalIF":1.4,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590037424000384/pdfft?md5=0ccbfff14c645a3ae81342d2cc1abe7a&pid=1-s2.0-S2590037424000384-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141478720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}