Journal of Mathematical Analysis and Applications最新文献

{"title":"Error estimates for the robust α-stable central limit theorem under sublinear expectation by a discrete approximation method","authors":"Lianzi Jiang","doi":"10.1016/j.jmaa.2024.129028","DOIUrl":"10.1016/j.jmaa.2024.129028","url":null,"abstract":"<div><div>In this work, we develop a numerical method to study the error estimates of the <em>α</em>-stable central limit theorem under sublinear expectation with <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, whose limit distribution can be characterized by a fully nonlinear integro-differential equation (PIDE). Based on the sequence of independent random variables, we propose a discrete approximation scheme for the fully nonlinear PIDE. With the help of the nonlinear stochastic analysis techniques and numerical analysis tools, we establish the error bounds for the discrete approximation scheme, which in turn provides a general error bound for the robust <em>α</em>-stable central limit theorem, including the integrable case <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> as well as the non-integrable case <span><math><mi>α</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span>. Finally, we provide some concrete examples to illustrate our main results and derive the precise convergence rates.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lump and interaction solutions to a (3+1)-dimensional BKP-Boussinesq-like equation","authors":"Xiyan Yang,&nbsp;Liangping Tang,&nbsp;Xinyi Gu,&nbsp;Wenxia Chen,&nbsp;Lixin Tian","doi":"10.1016/j.jmaa.2024.129030","DOIUrl":"10.1016/j.jmaa.2024.129030","url":null,"abstract":"<div><div>This paper analyzes the (3+1)-dimensional BKP-Boussinesq-like equation, which is widely used to describe and understand nonlinear wave phenomena. We extend Hirota's bilinear method and obtain the generalized bilinear operator. When the prime number <span><math><mi>p</mi><mo>=</mo><mn>3</mn></math></span>, the generalized bilinear form of BKP-Boussinesq-like equation is constructed. Based on its bilinear expression, we explore the lump and lump-soliton solutions to the equation, and analyze the dynamic characteristics and properties of soliton solutions with plots.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587093","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Isometries on Tsirelson-type spaces","authors":"A. Golbaharan ,&nbsp;S. Amiri","doi":"10.1016/j.jmaa.2024.129019","DOIUrl":"10.1016/j.jmaa.2024.129019","url":null,"abstract":"<div><div>We provide a characterization of the surjective linear isometries on certain sequence spaces that follow the Tsirelson norm.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A diffusive predator-prey system with hunting cooperation in predators and prey-taxis: I global existence and stability","authors":"Wonlyul Ko,&nbsp;Kimun Ryu","doi":"10.1016/j.jmaa.2024.129005","DOIUrl":"10.1016/j.jmaa.2024.129005","url":null,"abstract":"<div><div>In this paper, we present and investigate a generalized reaction-diffusion system of predator-prey dynamics that incorporates prey-taxis and a hunting cooperation effect in predators, subject to homogeneous Neumann boundary conditions. This system describes a predator-prey interaction, in which the prey exhibit group defense mechanisms against their predators, and the predators cooperate to hunt these defended prey. The mechanism of prey is implemented through the (repulsive) prey-taxis term, which affects the diffusion rate of the predators, while the hunting cooperation effect of the predators towards their prey is implemented through the functional response. Moreover, this system incorporates generalized functional forms for the prey's growth rate, the predators' functional response and mortality rate, and the prey-tactic sensitivity, allowing for adaptation to various scenarios. We first establish that solutions of the time- and space-dependent system with such ecological characteristics exist globally and are bounded by estimating an associated weighted integral. Secondly, we investigate the constant coexistence state of the generalized system by introducing a constructed function that incorporates the prey's growth rate, the predators' functional response and mortality rate. Finally, we find some conditions yielding the local stability of all feasible constant and nonnegative solutions of the system, thereby revealing the occurrence of bistability. Furthermore, we conduct an investigation into the global stability at both the constant coexistence and predator-free states by applying Lyapunov stability analysis. We also analyze the rate at which the solutions to the system converge to these steady-states by utilizing the boundedness of the solutions along with Gagliardo-Nirenberg inequality.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping","authors":"Hui Liu ,&nbsp;Chengfeng Sun ,&nbsp;Mei Li","doi":"10.1016/j.jmaa.2024.129007","DOIUrl":"10.1016/j.jmaa.2024.129007","url":null,"abstract":"<div><div>The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for <span><math><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and <span><math><mi>β</mi><mo>≥</mo><mn>4</mn></math></span>. Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>s</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> <span><math><mo>(</mo><mi>s</mi><mo>&gt;</mo><mn>2</mn><mo>)</mo></math></span> for <span><math><mi>α</mi><mo>≥</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math></span> and <span><math><mn>4</mn><mo>≤</mo><mi>β</mi><mo>≤</mo><mn>5</mn></math></span>.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Liouville-type theorems for partial trace equations with nonlinear gradient terms","authors":"Bukayaw Kindu ,&nbsp;Ahmed Mohammed ,&nbsp;Birilew Tsegaw","doi":"10.1016/j.jmaa.2024.129010","DOIUrl":"10.1016/j.jmaa.2024.129010","url":null,"abstract":"<div><div>In this paper, we will study various Liouville-type theorems for partial trace equations with nonlinear gradient terms. Specifically, we will provide sufficient conditions for non-negative viscosity subsolutions of these equations in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to vanish identically. For a prototype of such equations, we will give necessary and sufficient conditions for non-negative subsolutions in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span> to be identically zero.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global existence and time decay rate of classical solutions to a hybrid Vlasov-Fokker-Planck-MHD equations","authors":"Peng Jiang,&nbsp;Jiayu He","doi":"10.1016/j.jmaa.2024.129004","DOIUrl":"10.1016/j.jmaa.2024.129004","url":null,"abstract":"<div><div>In this paper, we prove the existence of global classical solutions to a kinetic-fluid system when initial data is a small perturbation of some given equilibrium state in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>. The system consists of the Vlasov-Fokker-Planck equation coupled with the compressible magnetohydrodynamics (MHD) equations via the nonlinear coupling terms of Lorenz force type. It describes the motion of energetic particles in a fluid with a magnetic field. The proof of global existence mainly relies on the energy method. Due to the complex nonlinear structure of Lorentz force, we need to establish a more refined uniform a prior estimates. Moreover, under additional conditions on initial data, the optimal time decay rate of solutions toward the equilibrium state can be obtained by using the Fourier analysis.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142593670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Zeros of a one-parameter family of rational harmonic trinomials","authors":"Linkui Gao ,&nbsp;Junyang Gao ,&nbsp;Gang Liu","doi":"10.1016/j.jmaa.2024.128997","DOIUrl":"10.1016/j.jmaa.2024.128997","url":null,"abstract":"<div><div>The number of zeros of a one-parameter family of rational harmonic trinomials is studied. It is considered to be as an analogue work on that of corresponding harmonic trinomials investigated recently by Brilleslyper et al. and Brooks et al. Note that their proofs rely on the Argument Principle for Harmonic Functions and involve finding the winding numbers about the origin of a hypocycloid. Our proof is similar by means of Poincaré index and the geometry of epicycloid.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142560565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Compact embedding from variable-order Sobolev space to Lq(x)(Ω) and its application to Choquard equation with variable order and variable critical exponent","authors":"Masaki Sakuma","doi":"10.1016/j.jmaa.2024.128999","DOIUrl":"10.1016/j.jmaa.2024.128999","url":null,"abstract":"<div><div>In this paper, we prove the compact embedding from the variable-order Sobolev space <span><math><msubsup><mrow><mi>W</mi></mrow><mrow><mn>0</mn></mrow><mrow><mi>s</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>,</mo><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> to the Nakano space <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></msup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span> with a critical exponent <span><math><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> satisfying some conditions. It is noteworthy that the embedding can be compact even when <span><math><mi>q</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></span> reaches the critical Sobolev exponent <span><math><msubsup><mrow><mi>p</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>⁎</mo></mrow></msubsup><mo>(</mo><mi>x</mi><mo>)</mo></math></span>. As an application, we obtain a nontrivial solution of the Choquard equation<span><span><span><math><msubsup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>p</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow><mrow><mi>s</mi><mo>(</mo><mo>⋅</mo><mo>,</mo><mo>⋅</mo><mo>)</mo></mrow></msubsup><mi>u</mi><mo>+</mo><mo>|</mo><mi>u</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>p</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>=</mo><mrow><mo>(</mo><munder><mo>∫</mo><mrow><mi>Ω</mi></mrow></munder><mfrac><mrow><mo>|</mo><mi>u</mi><mo>(</mo><mi>y</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>r</mi><mo>(</mo><mi>y</mi><mo>)</mo></mrow></msup></mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><msup><mrow><mo>|</mo></mrow><mrow><mfrac><mrow><mi>α</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>+</mo><mi>α</mi><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mrow></mfrac><mi>d</mi><mi>y</mi><mo>)</mo></mrow><mo>|</mo><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><msup><mrow><mo>|</mo></mrow><mrow><mi>r</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>x</mi><mo>)</mo><mspace></mspace><mrow><mtext>in </mtext><mi>Ω</mi></mrow></math></span></span></span> with variable upper critical exponent in the sense of Hardy-Littlewood-Sobolev inequality under an appropriate boundary condition.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142552185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Null-controllability and Carleman estimates for non-autonomous degenerate PDEs: A climatological application","authors":"Mohammad Akil ,&nbsp;Genni Fragnelli ,&nbsp;Sarah Ismail","doi":"10.1016/j.jmaa.2024.128984","DOIUrl":"10.1016/j.jmaa.2024.128984","url":null,"abstract":"<div><div>Inspired by a Budyko-Seller model, we consider non-autonomous degenerate parabolic equations. As a first step, using Kato's Theorem we prove the well-posedness of such problems. Then, obtaining new Carleman estimates for the non-homogeneous non-autonomous adjoint problems, we deduce null-controllability for the original ones. Some linear and semilinear extensions are also considered. We conclude the paper applying the obtained controllability result to the Budyko-Seller model given in the introduction.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142586029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}