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Journal of Mathematical Physics Analysis Geometry最新文献

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Riemann–Hilbert problem for the Fokas–Lenells equation in the presence of high-order discrete spectrum with non-vanishing boundary conditions 具有非消失边界条件的高阶离散谱的Fokas-Lenells方程的Riemann-Hilbert问题
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0097122
Xiao-fan Zhang, Shou‐Fu Tian
{"title":"Riemann–Hilbert problem for the Fokas–Lenells equation in the presence of high-order discrete spectrum with non-vanishing boundary conditions","authors":"Xiao-fan Zhang, Shou‐Fu Tian","doi":"10.1063/5.0097122","DOIUrl":"https://doi.org/10.1063/5.0097122","url":null,"abstract":"We extend the Riemann–Hilbert (RH) method to study the Fokas–Lenells (FL) equation with nonzero boundary conditions at infinity and successfully find its multiple soliton solutions with one high-order pole and N high-order poles. The mathematical structures of the FL equation are constructed, including global conservation laws and local conservation laws. Then, the conditions (analytic, symmetric, and asymptotic properties) needed to construct the RH problem are obtained by analyzing the spectral problem. The reflection coefficient r(z) with two cases appearing in the RH problem is considered, including one high-order pole and N high-order poles. In order to overcome the difficulty of establishing the residue expressions corresponding to high-order poles, we introduce the generalized residue formula. Finally, the expression of exact soliton solutions with reflectionless potential is further derived by a closed algebraic system.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"47 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87344866","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Qualitative properties of solution to a viscoelastic Kirchhoff-like plate equation 粘弹性类kirchhoff板方程解的定性性质
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0149240
Yang Liu, Byungsoo Moon, Vicentiu D. Rădulescu, Runzhang Xu, Chao Yang
{"title":"Qualitative properties of solution to a viscoelastic Kirchhoff-like plate equation","authors":"Yang Liu, Byungsoo Moon, Vicentiu D. Rădulescu, Runzhang Xu, Chao Yang","doi":"10.1063/5.0149240","DOIUrl":"https://doi.org/10.1063/5.0149240","url":null,"abstract":"This paper is concerned with the initial boundary value problem for viscoelastic Kirchhoff-like plate equations with rotational inertia, memory, p-Laplacian restoring force, weak damping, strong damping, and nonlinear source terms. We establish the local existence and uniqueness of the solution by linearization and the contraction mapping principle. Then, we obtain the global existence of solutions with subcritical and critical initial energy by applying potential well theory. Then, we prove the asymptotic behavior of the global solution with positive initial energy strictly below the depth of the potential well. Finally, we conduct a comprehensive study on the finite time blow-up of solutions with negative initial energy, null initial energy, and positive initial energy strictly below the depth of the potential well and arbitrary positive initial energy, respectively.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"19 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82881323","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Self-intersection local time derivative for systems of non-linear stochastic heat equations 非线性随机热方程系统的自交局部时间导数
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0117488
Qian Yu
{"title":"Self-intersection local time derivative for systems of non-linear stochastic heat equations","authors":"Qian Yu","doi":"10.1063/5.0117488","DOIUrl":"https://doi.org/10.1063/5.0117488","url":null,"abstract":"We consider the existence and Hölder continuity conditions for the higher-order derivative of self-intersection local time for u(t, x), where u(t,x)=u1(t,x),…,ud(t,x) is the solution to a system of non-linear stochastic heat equations driven by a d-dimensional space-time white noise. Moreover, we study the cases of intersection local time and collision local time.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"68 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80597060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiple mixed interior and boundary peaks synchronized solutions for nonlinear coupled elliptic systems 非线性耦合椭圆型系统的多重混合内峰和边界峰同步解
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0120617
Z. Tang, Lushun Wang, Huafei Xie
{"title":"Multiple mixed interior and boundary peaks synchronized solutions for nonlinear coupled elliptic systems","authors":"Z. Tang, Lushun Wang, Huafei Xie","doi":"10.1063/5.0120617","DOIUrl":"https://doi.org/10.1063/5.0120617","url":null,"abstract":"This paper is devoted to a class of singularly perturbed nonlinear Schrödinger systems defined on a smooth bounded domain in RN(N=2,3). We use the Lyapunov–Schmidt reduction method to construct synchronized vector solutions with multiple spikes both on the boundary and in the interior of the domain. For each vector solution that has been constructed, we point out that the interior spikes locate near sphere packing points in the domain, and the boundary spikes locate near the critical points of the mean curvature function related to the boundary of the domain.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"48 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81002476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Renormalized non-negative solutions for the double phase Dirichlet problems with L1 data 带L1数据的双相Dirichlet问题的重整化非负解
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0145741
B. Ge, Qing-Hai Cao, Yu Zhang
{"title":"Renormalized non-negative solutions for the double phase Dirichlet problems with L1 data","authors":"B. Ge, Qing-Hai Cao, Yu Zhang","doi":"10.1063/5.0145741","DOIUrl":"https://doi.org/10.1063/5.0145741","url":null,"abstract":"This article investigates a class of double phase problem with L1 data. Some new criteria to guarantee that the existence and uniqueness of non-negative renormalized solutions for the considered problem are established by using the approximation and energy methods.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"116 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87727175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Optimal well-posedness for the pressureless Euler–Navier–Stokes system 无压Euler-Navier-Stokes系统的最优适定性
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0136429
Xiaoping Zhai, Yiren Chen, Yongsheng Li, Yongye Zhao
{"title":"Optimal well-posedness for the pressureless Euler–Navier–Stokes system","authors":"Xiaoping Zhai, Yiren Chen, Yongsheng Li, Yongye Zhao","doi":"10.1063/5.0136429","DOIUrl":"https://doi.org/10.1063/5.0136429","url":null,"abstract":"In this work, we investigate the Cauchy problem for the pressureless Euler–Navier–Stokes system in R3. We first establish the global small solutions of this system with critical regularity and then obtain the optimal time decay rate of the solutions by a suitable energy argument (independent of the spectral analysis). The proof crucially depends on non-standard product estimates and interpolations. In comparison with previous studies about time-decay by Choi and Jung [J. Math. Fluid Mech. 23, 99 (2021); arXiv:2112.14449], the smallness requirement of the low frequencies of initial data could be removed.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"78 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84659736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Liouville type theorem and Morse indices of a semilinear elliptic equation with nonlocal nonlinearities 一类具有非局部非线性的半线性椭圆方程的Liouville型定理和Morse指标
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0091269
Xiaowei An, Huixia He, Xianfa Song
{"title":"Liouville type theorem and Morse indices of a semilinear elliptic equation with nonlocal nonlinearities","authors":"Xiaowei An, Huixia He, Xianfa Song","doi":"10.1063/5.0091269","DOIUrl":"https://doi.org/10.1063/5.0091269","url":null,"abstract":"In this study, we study the solution of a semilinear elliptic equation with nonlocal nonlinearities. By using the mountain pass theorem, Hölder’s inequality, and Sobolev embedding theorem, we obtain the existence result, establish the Liouville type theorem, and consider Morse indices of the equation.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"105 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90967691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Pathwise unstable invariant manifolds reduction for stochastic evolution equations driven by nonlinear noise 非线性噪声驱动下随机演化方程的路径不稳定不变流形约简
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0101516
Xuewei Ju
{"title":"Pathwise unstable invariant manifolds reduction for stochastic evolution equations driven by nonlinear noise","authors":"Xuewei Ju","doi":"10.1063/5.0101516","DOIUrl":"https://doi.org/10.1063/5.0101516","url":null,"abstract":"This paper is concerned with the pathwise dynamics of the stochastic evolution equation: du + Audt = F(u)dt + G(u)dW(t) on a separable Hilbert space H with the Lipschitz continuous drift term F(u) as well as the Lipschitz continuous diffusion term G(u). We first introduce the notion of generalized random dynamical systems (GRDSs) and show that the equation can generate a GRDS. We then construct a pathwise unstable manifold for the GRDS provided that the Lipschitz constants of the drift term and the diffusion term satisfy a spectral gap condition. At last, we present a pathwise unstable manifold reduction for the GRDS.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"45 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86526386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dubrovin–Frobenius manifolds associated with Bn and the constrained KP hierarchy 与Bn相关的Dubrovin-Frobenius流形和受限KP层次
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0142578
Shilin Ma, Dafeng Zuo
{"title":"Dubrovin–Frobenius manifolds associated with Bn and the constrained KP hierarchy","authors":"Shilin Ma, Dafeng Zuo","doi":"10.1063/5.0142578","DOIUrl":"https://doi.org/10.1063/5.0142578","url":null,"abstract":"In this paper, we will show that the Dubrovin–Frobenius prepotentials on the orbit space of the Coxeter group Bn constructed by Arsie et al. [Sel. Math. New Ser. 29, 1 (2023)] coincide with the solutions of Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations associated with the constrained KP hierarchy.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"38 9-10","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72608353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Boundedness of atmospheric Ekman flows with two-layer eddy viscosity 两层涡旋黏度下大气Ekman流动的有界性
IF 0.5 4区 数学
Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-05-01 DOI: 10.1063/5.0142172
Y. Guan
{"title":"Boundedness of atmospheric Ekman flows with two-layer eddy viscosity","authors":"Y. Guan","doi":"10.1063/5.0142172","DOIUrl":"https://doi.org/10.1063/5.0142172","url":null,"abstract":"In this paper, we study the boundedness of atmospheric Ekman flows with classical boundary conditions. We consider the system with a two-layer eddy viscosity, consisting of a constant eddy viscosity in the upper layer and a continuous eddy viscosity in the lower layer. We analyze the boundedness of the solution by using the logarithmic matrix norm.","PeriodicalId":50141,"journal":{"name":"Journal of Mathematical Physics Analysis Geometry","volume":"3 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74346333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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