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Nonlinear Differential Equations and Applications (NoDEA)最新文献

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A note on averaging for the dispersion-managed NLS 关于分散管理 NLS 平均法的说明
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-09-16 DOI: 10.1007/s00030-024-00994-9
Jason Murphy
{"title":"A note on averaging for the dispersion-managed NLS","authors":"Jason Murphy","doi":"10.1007/s00030-024-00994-9","DOIUrl":"https://doi.org/10.1007/s00030-024-00994-9","url":null,"abstract":"<p>We discuss averaging for dispersion-managed nonlinear Schrödinger equations in the fast dispersion management regime,with an application to the problem of constructing soliton-like solutions to dispersion-managed nonlinear Schrödinger equations.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"2 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260042","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global regularity of 2D generalized incompressible magnetohydrodynamic equations 二维广义不可压缩磁流体动力学方程的全局正则性
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-09-14 DOI: 10.1007/s00030-024-00995-8
Chao Deng, Zhuan Ye, Baoquan Yuan, Jiefeng Zhao
{"title":"Global regularity of 2D generalized incompressible magnetohydrodynamic equations","authors":"Chao Deng, Zhuan Ye, Baoquan Yuan, Jiefeng Zhao","doi":"10.1007/s00030-024-00995-8","DOIUrl":"https://doi.org/10.1007/s00030-024-00995-8","url":null,"abstract":"<p>In this paper, we are concerned with the two-dimensional (2D) incompressible magnetohydrodynamic (MHD) equations with velocity dissipation given by <span>((-Delta )^{alpha })</span> and magnetic diffusion given by reducing about the square root of logarithmic diffusion from standard Laplacian diffusion. More precisely, we establish the global regularity of solutions to the system as long as the power <span>(alpha )</span> is a positive constant. In addition, we prove several global a priori bounds for the case <span>(alpha =0)</span>. Finally, for the case <span>(alpha =0)</span>, it is also shown that the control of the direction of the magnetic field in a suitable norm is enough to guarantee the global regularity. In particular, our results significantly improve previous works and take us one step closer to a complete resolution of the global regularity issue on the 2D resistive MHD equations, namely, the case when the MHD equations only have standard Laplacian magnetic diffusion.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Classical and generalized solutions of an alarm-taxis model 警报-出租车模型的经典解法和广义解法
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-16 DOI: 10.1007/s00030-024-00989-6
Mario Fuest, Johannes Lankeit
{"title":"Classical and generalized solutions of an alarm-taxis model","authors":"Mario Fuest, Johannes Lankeit","doi":"10.1007/s00030-024-00989-6","DOIUrl":"https://doi.org/10.1007/s00030-024-00989-6","url":null,"abstract":"<p>In bounded, spatially two-dimensional domains, the system </p><p>complemented with initial and homogeneous Neumann boundary conditions, models the interaction between prey (with density <i>u</i>), predator (with density <i>v</i>) and superpredator (with density <i>w</i>), which preys on both other populations. Apart from random motion and prey-tactical behavior of the primary predator, the key aspect of this system is that the secondary predator reacts to alarm calls of the prey, issued by the latter whenever attacked by the primary predator. We first show in the pure alarm-taxis model, i.e. if <span>(xi = 0)</span>, that global classical solutions exist. For the full model (with <span>(xi &gt; 0)</span>), the taxis terms and the presence of the term <span>(-a_2 uw)</span> in the first equation apparently hinder certain bootstrap procedures, meaning that the available regularity information is rather limited. Nonetheless, we are able to obtain global generalized solutions. An important technical challenge is to guarantee strong convergence of (weighted) gradients of the first two solution components in order to conclude that approximate solutions converge to a generalized solution of the limit problem.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sign-changing solution for an elliptic equation with critical growth at the boundary 边界有临界增长的椭圆方程的符号变化解
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-14 DOI: 10.1007/s00030-024-00990-z
Marcelo F. Furtado, João Pablo Pinheiro da Silva, Karla Carolina V. De Sousa
{"title":"Sign-changing solution for an elliptic equation with critical growth at the boundary","authors":"Marcelo F. Furtado, João Pablo Pinheiro da Silva, Karla Carolina V. De Sousa","doi":"10.1007/s00030-024-00990-z","DOIUrl":"https://doi.org/10.1007/s00030-024-00990-z","url":null,"abstract":"<p>We prove the existence of sign-changing solution to the problem </p><span>$$begin{aligned} -Delta u-dfrac{1}{2}left( xcdot nabla uright) =lambda u, hbox { in }mathbb {R}_{+}^{N}, qquad dfrac{partial u}{partial nu }=|u|^{2_*-2}u, hbox { on } partial mathbb {R}_{+}^{N}, end{aligned}$$</span><p>where <span>(mathbb {R}^N_+ = {(x',x_N): x' in mathbb {R}^{N-1},,x_N&gt;0 })</span> is the upper half-space, <span>(2_*:=2(N-1)/(N-2))</span>, <span>(N ge 7)</span>, <span>(frac{partial u}{partial nu })</span> is the partial outward normal derivative and the parameter <span>(lambda &gt;0)</span> interacts with the spectrum of the linearized problem. In the proof, we apply variational methods.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"154 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142180056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
New critical point theorem and infinitely many normalized small-magnitude solutions of mass supercritical Schrödinger equations 质量超临界薛定谔方程的新临界点定理和无限多归一化小幅解
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-08 DOI: 10.1007/s00030-024-00988-7
Shaowei Chen
{"title":"New critical point theorem and infinitely many normalized small-magnitude solutions of mass supercritical Schrödinger equations","authors":"Shaowei Chen","doi":"10.1007/s00030-024-00988-7","DOIUrl":"https://doi.org/10.1007/s00030-024-00988-7","url":null,"abstract":"<p>In this study, we investigate the existence of solutions <span>((lambda , u) in mathbb {R} times H^1(mathbb {R}^N))</span> to the Schrödinger equation </p><span>$$begin{aligned} left{ begin{array}{ll} -Delta u+V(x)u+lambda u=|u|^{p-2}u,quad xin mathbb {R}^{N}, int _{mathbb {R}^N}|u|^2=a, end{array} right. end{aligned}$$</span><p>where <span>(Nge 2)</span>, <span>(a&gt;0)</span> is a constant and <i>p</i> satisfies <span>(2+4/N&lt;p&lt;+infty )</span>. The potential <i>V</i> satisfies the condition that the operator <span>(-Delta +V)</span> contains infinitely many isolated eigenvalues with an accumulation point. We prove that this equation has a sequence of solutions <span>({(lambda _m, u_m)})</span> such that <span>(Vert u_mVert _{L^infty (mathbb {R}^N)}rightarrow 0)</span> as <span>(mrightarrow infty )</span>. The proof is provided by establishing a new critical point theorem without the typical Palais–Smale condition.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"79 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941777","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs 路径依赖的汉密尔顿-雅各比-贝尔曼 PDE 的 Crandall-Lions 粘度解的收敛定理
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-04 DOI: 10.1007/s00030-024-00986-9
David Criens
{"title":"A convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs","authors":"David Criens","doi":"10.1007/s00030-024-00986-9","DOIUrl":"https://doi.org/10.1007/s00030-024-00986-9","url":null,"abstract":"<p>We establish a convergence theorem for Crandall–Lions viscosity solutions to path-dependent Hamilton–Jacobi–Bellman PDEs. Our proof is based on a novel convergence theorem for dynamic sublinear expectations and the stochastic representation of viscosity solutions as value functions.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Elastic flow of curves with partial free boundary 部分自由边界曲线的弹性流动
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-01 DOI: 10.1007/s00030-024-00984-x
Antonia Diana
{"title":"Elastic flow of curves with partial free boundary","authors":"Antonia Diana","doi":"10.1007/s00030-024-00984-x","DOIUrl":"https://doi.org/10.1007/s00030-024-00984-x","url":null,"abstract":"<p>We consider a curve with boundary points free to move on a line in <span>({{{mathbb {R}}}}^2)</span>, which evolves by the <span>(L^2)</span>-gradient flow of the elastic energy, that is, a linear combination of the Willmore and the length functional. For this planar evolution problem, we study the short and long-time existence. Once we establish under which boundary conditions the PDE’s system is well-posed (in our case the Navier boundary conditions), employing the Solonnikov theory for linear parabolic systems in Hölder space, we show that there exists a unique flow in a maximal time interval [0, <i>T</i>). Then, using energy methods we prove that the maximal time is <span>(T= + infty )</span>.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"160 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869380","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups 卡诺群中不连续汉密尔顿-雅可比方程的 Monge 解决方案
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-08-01 DOI: 10.1007/s00030-024-00983-y
Fares Essebei, Gianmarco Giovannardi, Simone Verzellesi
{"title":"Monge solutions for discontinuous Hamilton-Jacobi equations in Carnot groups","authors":"Fares Essebei, Gianmarco Giovannardi, Simone Verzellesi","doi":"10.1007/s00030-024-00983-y","DOIUrl":"https://doi.org/10.1007/s00030-024-00983-y","url":null,"abstract":"<p>In this paper we study Monge solutions to stationary Hamilton–Jacobi equations associated to discontinuous Hamiltonians in the framework of Carnot groups. After showing the equivalence between Monge and viscosity solutions in the continuous setting, we prove existence and uniqueness for the Dirichlet problem, together with a comparison principle and a stability result.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"217 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873163","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Control sets of linear control systems on $$mathbb {R}^2$$ . The real case $$mathbb {R}^2$$ 上线性控制系统的控制集 .实际情况
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-07-29 DOI: 10.1007/s00030-024-00987-8
Víctor Ayala, Adriano Da Silva, Anderson F. P. Rojas
{"title":"Control sets of linear control systems on $$mathbb {R}^2$$ . The real case","authors":"Víctor Ayala, Adriano Da Silva, Anderson F. P. Rojas","doi":"10.1007/s00030-024-00987-8","DOIUrl":"https://doi.org/10.1007/s00030-024-00987-8","url":null,"abstract":"<p>In this paper, we study the dynamical behavior of a linear control system on <span>(mathbb {R}^2)</span> when the associated matrix has real eigenvalues. Different from the complex case, we show that the position of the control zero relative to the control range can have a strong interference in such dynamics if the matrix is not invertible. In the invertible case, we explicitly construct the unique control set with a nonempty interior.</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"74 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141869378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The cubic-quintic nonlinear Schrödinger equation with inverse-square potential 具有反平方势的三次-五次非线性薛定谔方程
Nonlinear Differential Equations and Applications (NoDEA) Pub Date : 2024-07-18 DOI: 10.1007/s00030-024-00979-8
Alex H. Ardila, Jason Murphy
{"title":"The cubic-quintic nonlinear Schrödinger equation with inverse-square potential","authors":"Alex H. Ardila, Jason Murphy","doi":"10.1007/s00030-024-00979-8","DOIUrl":"https://doi.org/10.1007/s00030-024-00979-8","url":null,"abstract":"<p>We consider the nonlinear Schrödinger equation in three space dimensions with a focusing cubic nonlinearity and defocusing quintic nonlinearity and in the presence of an external inverse-square potential. We establish scattering in the region of the mass-energy plane where the virial functional is guaranteed to be positive. Our result parallels the scattering result of [11] in the setting of the standard cubic-quintic NLS.\u0000</p>","PeriodicalId":501665,"journal":{"name":"Nonlinear Differential Equations and Applications (NoDEA)","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141742985","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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