Applied Mathematics Letters最新文献

{"title":"Radial solutions for Neumann problems involving prescribed mean curvature operator in a ball and in an annular domain","authors":"","doi":"10.1016/j.aml.2024.109256","DOIUrl":"10.1016/j.aml.2024.109256","url":null,"abstract":"<div><p>Using topological transversality method together with barrier strip technique and cut-off technique, we obtain new existence and uniqueness results of radial solutions to the Neumann problems involving prescribed mean curvature operator <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mtext>div</mtext><mfenced><mrow><mfrac><mrow><mo>∇</mo><mi>v</mi></mrow><mrow><msqrt><mrow><mn>1</mn><mo>+</mo><msup><mrow><mrow><mo>|</mo><mo>∇</mo><mi>v</mi><mo>|</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup></mrow></msqrt></mrow></mfrac></mrow></mfenced><mo>=</mo><mi>f</mi><mfenced><mrow><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>,</mo><mi>v</mi><mo>,</mo><mfrac><mrow><mi>d</mi><mi>v</mi></mrow><mrow><mi>d</mi><mi>r</mi></mrow></mfrac></mrow></mfenced><mspace></mspace><mi>i</mi><mi>n</mi><mspace></mspace><mi>Ω</mi><mo>,</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mi>∂</mi><mi>v</mi></mrow><mrow><mi>∂</mi><mi>n</mi></mrow></mfrac><mo>=</mo><mn>0</mn><mspace></mspace><mi>o</mi><mi>n</mi><mspace></mspace><mi>∂</mi><mi>Ω</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><mi>Ω</mi><mo>=</mo><mrow><mo>{</mo><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>:</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>&lt;</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>}</mo></mrow><mrow><mo>(</mo><mn>0</mn><mo>≤</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><mi>N</mi><mo>≥</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, <span><math><mrow><mi>f</mi><mo>:</mo><mrow><mo>[</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo></mrow><mo>×</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>→</mo><mi>R</mi></mrow></math></span> is continuous. Meanwhile, we demonstrate the importance of our results through an illustrative example.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Some properties of solutions to the integrable Camassa–Holm type equation","authors":"","doi":"10.1016/j.aml.2024.109247","DOIUrl":"10.1016/j.aml.2024.109247","url":null,"abstract":"<div><p>In this paper, we study an integrable Camassa–Holm type equation. We proved that if the initial datum <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>⁄</mo><mo>≡</mo><mn>0</mn></mrow></math></span> is compactly supported in <span><math><mrow><mo>[</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>]</mo></mrow></math></span>; then the corresponding solution to the Camassa–Holm type equation has the following property: <span><span><span><math><mrow><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><mfenced><mrow><mtable><mtr><mtd><mn>0</mn><mo>,</mo></mtd><mtd><mi>x</mi><mo>&gt;</mo><mi>q</mi><mrow><mo>(</mo><mi>c</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>;</mo></mtd></mtr><mtr><mtd><mi>l</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mrow><mi>e</mi></mrow><mrow><mi>x</mi></mrow></msup><mo>,</mo></mtd><mtd><mi>x</mi><mo>&lt;</mo><mi>q</mi><mrow><mo>(</mo><mi>a</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>.</mo></mtd></mtr></mtable></mrow></mfenced></mrow></math></span></span></span>Furthermore, <span><math><mrow><mi>l</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>&lt;</mo><mn>0</mn></mrow></math></span> is a continuous non-vanishing function and strictly decreasing. Long time behavior for the support of momentum density is also studied.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The mass- and energy-conserving relaxation virtual element method for the nonlinear Schrödinger equation","authors":"","doi":"10.1016/j.aml.2024.109251","DOIUrl":"10.1016/j.aml.2024.109251","url":null,"abstract":"<div><p>This paper develops a conservative relaxation virtual element method for the nonlinear Schrödinger equation on polygonal meshes. The advantage of this method is to build the virtual element space where the basis functions do not need to be explicitly defined for each local element, and the bilinear forms and nonlinear terms can be computed by using elementwise polynomial projections and pre-defined degrees of freedom. Furthermore, the constructed schemes ensure the conservation of both mass and energy in discrete senses. By using the Brouwer fixed point theorem, we prove the unique solvability of the fully discrete scheme. Finally, some numerical experiments are implemented to verify the theoretical results.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lifespan of solutions for a class of fourth order parabolic equations involving the Hessian","authors":"","doi":"10.1016/j.aml.2024.109253","DOIUrl":"10.1016/j.aml.2024.109253","url":null,"abstract":"<div><p>This paper deals with blow-up solutions of a class of initial–boundary value problems for a fourth order parabolic equation involving the Hessian. A lower bound for the lifespan of such solutions is derived.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0893965924002738/pdfft?md5=75581c0da645cd946b9d845d0ad269cd&pid=1-s2.0-S0893965924002738-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Periodic wave solutions for a generalized reaction–convection–diffusion equation of high-order","authors":"","doi":"10.1016/j.aml.2024.109249","DOIUrl":"10.1016/j.aml.2024.109249","url":null,"abstract":"<div><p>In this paper, we investigate the uniqueness of periodic wave solutions for a generalized reaction–convection–diffusion equation with arbitrarily high-order reaction term or convection term. The main technique is to prove the monotonicity of the ratio of two Abelian integrals by a new criterion and Descartes’ rule of signs. A positive answer to a conjecture stated in Wei and Chen (2023) is given and some numeric simulations are carried out to illustrate the obtained theoretical results.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141891983","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unconditionally convergent τ splitting iterative methods for variable coefficient Riesz space fractional diffusion equations","authors":"","doi":"10.1016/j.aml.2024.109252","DOIUrl":"10.1016/j.aml.2024.109252","url":null,"abstract":"<div><p>In this paper, we consider fast solvers for discrete linear systems generated by Riesz space fractional diffusion equations. We extract a scalar matrix, a compensation matrix, and a <span><math><mi>τ</mi></math></span> matrix from the coefficient matrix, and use their sum to construct a class of <span><math><mi>τ</mi></math></span> splitting iterative methods. Additionally, we design a preconditioner for the conjugate gradient method. Theoretical analyses show that the proposed <span><math><mi>τ</mi></math></span> splitting iterative methods are unconditionally convergent with convergence rates independent of step-sizes. Numerical results are provided to demonstrate the effectiveness of the proposed iterative methods.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910623","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A linear second-order maximum bound principle preserving finite difference scheme for the generalized Allen–Cahn equation","authors":"","doi":"10.1016/j.aml.2024.109250","DOIUrl":"10.1016/j.aml.2024.109250","url":null,"abstract":"<div><p>In this paper, we consider the numerical method for generalized Allen–Cahn equation with nonlinear mobility and convection term. We propose a linear second-order finite difference scheme which preserves the discrete maximum bound principle (MBP). The scheme is discretized by stabilized Crank–Nicolson in time, upwind scheme for convection term and central-difference scheme for diffusion term. We show that the proposed scheme preserves the discrete MBP under some constraints on temporal step size and stabilizing parameter. Optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup></math></span>-error estimate is obtained for our scheme. Several numerical experiments are performed to validate our theoretical results.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910589","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Local well-posedness of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator","authors":"","doi":"10.1016/j.aml.2024.109248","DOIUrl":"10.1016/j.aml.2024.109248","url":null,"abstract":"<div><p>Based on the local well-posedness for the homogeneous abstract problem, the existence and uniqueness of the local mild and classical solutions have been presented by using Kato’s variable norm technique for the Cauchy problem of abstract hyperbolic equation with Lipschitz perturbation and non-autonomous operator.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141910628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Critical points, stability, and basins of attraction of three Kuramoto oscillators with isosceles triangle network","authors":"","doi":"10.1016/j.aml.2024.109246","DOIUrl":"10.1016/j.aml.2024.109246","url":null,"abstract":"<div><p>We investigate the Kuramoto model with three oscillators interconnected by an isosceles triangle network. The characteristic of this model is that the coupling connections between the oscillators can be either attractive or repulsive. We list all critical points and investigate their stability. We furthermore present a framework studying convergence towards stable critical points under special coupled strengths. The main tool is the linearization and the monotonicity arguments of oscillator diameter.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic dynamics on HBV infection in vivo with interval delay","authors":"","doi":"10.1016/j.aml.2024.109234","DOIUrl":"10.1016/j.aml.2024.109234","url":null,"abstract":"<div><p>Because noise is ubiquitous within-host, a stochastic dynamical system with interval delay is proposed to model the dynamics of HBV infection in vivo. The global existence and nonnegativity of the solutions are established. Virus extinction conditions are derived, under which the asymptotic properties of the virus-free equilibrium are proved, and the persistence conditions are obtained. Finally, numerical simulations are performed to examine the influence of noise on the Hopf bifurcation resulting from the delay parameters in the interval delay.</p></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141839833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}