Journal of Dynamics and Differential Equations最新文献

On the effect of randomization on supercritical heat equations. 随机化对超临界热方程的影响。

IF 1.1 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2026-01-01 Epub Date: 2026-05-06 DOI: 10.1007/s10884-026-10511-4

Eliseo Luongo

{"title":"On the effect of randomization on supercritical heat equations.","authors":"Eliseo Luongo","doi":"10.1007/s10884-026-10511-4","DOIUrl":"https://doi.org/10.1007/s10884-026-10511-4","url":null,"abstract":"Recently, in Glogić et al. (Non-uniqueness of mild solutions to supercritical heat equations. arXiv:2501.17032 (2025)), it has been shown that the focusing power nonlinearity heat equation <dispformula> <math> <mrow> <mtable> <mtr> <mtd> <mrow><msub><mi>∂</mi> <mi>t</mi></msub> <mi>u</mi> <mo>-</mo> <mi>Δ</mi> <mi>u</mi> <mo>=</mo> <msup><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow> <mrow><mi>p</mi> <mo>-</mo> <mn>1</mn></mrow> </msup> <mi>u</mi> <mo>,</mo> <mspace></mspace> <mi>p</mi> <mo>></mo> <mn>1</mn> <mo>,</mo></mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> in dimensions <math><mrow><mi>d</mi> <mo>≥</mo> <mn>3</mn></mrow> </math> has non-unique local solutions in <math> <mrow><msup><mi>L</mi> <mi>q</mi></msup> <mrow><mo>(</mo> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> <mo>)</mo></mrow> </mrow> </math> for <math><mrow><mi>q</mi> <mo><</mo> <mi>d</mi> <mo>(</mo> <mi>p</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> <mo>/</mo> <mn>2</mn></mrow> </math> provided that <math><mrow><mi>p</mi> <mo><</mo> <msub><mi>p</mi> <mrow><mi>JL</mi></mrow> </msub> </mrow> </math> , where <math><msub><mi>p</mi> <mrow><mi>JL</mi></mrow> </msub> </math> denotes the Joseph-Lundgren exponent. In this paper we investigate the effect of different randomizations on the well-posedness of the equation. First we show that adding a forcing term white in time and colored in space in (NLH) is not sufficient to improve the solution theory: namely, we prove non-uniqueness for local-in-time mild solutions of (NLH) with additive noise. Second, we discuss how randomizing the initial conditions of (NLH) affects its well-posedness.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"38 Suppl 1","pages":"491-521"},"PeriodicalIF":1.1,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13658471/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149182024","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A Remark on the Log-Sobolev Inequality for the Gibbs Measure of the Focusing Schrödinger Equation. 聚焦Schrödinger方程Gibbs测度的Log-Sobolev不等式的注解。

IF 1.1 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2026-01-01 Epub Date: 2026-04-25 DOI: 10.1007/s10884-026-10509-y

Guopeng Li, Jiawei Li, Leonardo Tolomeo

{"title":"A Remark on the Log-Sobolev Inequality for the Gibbs Measure of the Focusing Schrödinger Equation.","authors":"Guopeng Li, Jiawei Li, Leonardo Tolomeo","doi":"10.1007/s10884-026-10509-y","DOIUrl":"https://doi.org/10.1007/s10884-026-10509-y","url":null,"abstract":"We consider the question of showing a log-Sobolev inequality for the Gibbs measure of the focusing Schrödinger equation built by Lebowitz-Rose-Speer (1988), formally given by <dispformula> <math> <mrow> <mtable> <mtr> <mtd><mrow><mi>d</mi> <mi>ρ</mi> <mo>∝</mo> <mo>exp</mo> <mrow><mo>(</mo></mrow> <mfrac><mn>1</mn> <mi>p</mi></mfrac> <msub><mo>∫</mo> <mi>T</mi></msub> <msup><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow> <mi>p</mi></msup> <mi>d</mi> <mi>x</mi> <mo>-</mo> <mfrac><mn>1</mn> <mn>2</mn></mfrac> <msub><mo>∫</mo> <mi>T</mi></msub> <msup><mrow><mo>|</mo> <mi>∇</mi> <mi>u</mi> <mo>|</mo></mrow> <mn>2</mn></msup> <mi>d</mi> <mi>x</mi> <mo>-</mo> <mfrac><mn>1</mn> <mn>2</mn></mfrac> <msub><mo>∫</mo> <mi>T</mi></msub> <msup><mrow><mo>|</mo> <mi>u</mi> <mo>|</mo></mrow> <mn>2</mn></msup> <mi>d</mi> <mi>x</mi> <mrow><mo>)</mo></mrow> <msub><mn>1</mn> <mrow> <msubsup><mrow><mo>‖</mo> <mi>u</mi> <mo>‖</mo></mrow> <mrow><msup><mi>L</mi> <mn>2</mn></msup> <mrow><mo>(</mo> <mi>T</mi> <mo>)</mo></mrow> </mrow> <mn>2</mn></msubsup> <mo>≤</mo> <mi>K</mi></mrow> </msub> <mi>d</mi> <mi>u</mi> <mi>d</mi> <mover><mi>u</mi> <mo>¯</mo></mover> <mo>.</mo></mrow> </mtd> </mtr> </mtable> </mrow> </math> </dispformula> When <math><mrow><mn>2</mn> <mo>≤</mo> <mi>p</mi> <mo>≤</mo> <mn>4</mn></mrow> </math> , we show that these measures indeed satisfy a log-Sobolev inequality. When <math><mrow><mi>p</mi> <mo>></mo> <mn>4</mn></mrow> </math> , we establish a lower bound for the Hessian of the effective potential. This implies that the known convexity-based multiscale techniques for the log-Sobolev inequalities cannot be applied to the measure <math><mi>ρ</mi></math> .","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"38 Suppl 1","pages":"455-471"},"PeriodicalIF":1.1,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13658493/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149181881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Three-dimensional exponential mixing and ideal kinematic dynamo with randomized ABC flows. 随机ABC流的三维指数混合与理想运动发电机。

IF 1.1 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2026-01-01 Epub Date: 2026-02-06 DOI: 10.1007/s10884-026-10483-5

Michele Coti Zelati, Víctor Navarro-Fernández

引用次数: 0

Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity u ¯ 2 in Negative Sobolev Spaces. 负Sobolev空间二次非线性$$overline{u}^2$$周期非线性Schrödinger方程的局部适定性

IF 1.1 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2025-01-01 Epub Date: 2023-08-07 DOI: 10.1007/s10884-023-10295-x

Ruoyuan Liu

引用次数: 0

Surfaces with Central Configuration and Dulac’s Problem for a Three Dimensional Isolated Hopf Singularity 具有中心配置的曲面和三维孤立霍普夫奇点的杜拉克问题

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-09-16 DOI: 10.1007/s10884-024-10377-4

Nuria Corral, María Martín-Vega, Fernando Sanz Sánchez

引用次数: 0

The Integral Manifolds of the 4 Body Problem with Equal Masses: Bifurcations at Relative Equilibria 质量相等的四体问题的积分漫域：相对平衡点的分岔

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-09-09 DOI: 10.1007/s10884-024-10391-6

Christopher K. McCord

{"title":"The Integral Manifolds of the 4 Body Problem with Equal Masses: Bifurcations at Relative Equilibria","authors":"Christopher K. McCord","doi":"10.1007/s10884-024-10391-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10391-6","url":null,"abstract":"In the N-body problem, it is classical that there are conserved quantities of center of mass, linear momentum, angular momentum and energy. The level sets (mathfrak {M}(c,h)) of these conserved quantities are parameterized by the angular momentum c and the energy h, and are known as the integral manifolds. A long-standing goal has been to identify the bifurcation values, especially the bifurcation values of energy for fixed non-zero angular momentum, and to describe the integral manifolds at the regular values. Alain Albouy identified two categories of singular values of energy: those corresponding to bifurcations at relative equilibria; and those corresponding to “bifurcations at infinity”, and demonstrated that these are the only possible bifurcation values. This work completes the identification of bifurcations for the four-body problem with equal masses, confirming that, in this setting, Albouy’s necessary conditions for bifurcation are also sufficient conditions: bifurcations of the integral manifolds occur at all of the singular values of energy. A recent study examined the bifurcations at infinity; this work evaluates the four bifurcations at relative equilibria. To establish that the topology of the integral manifolds changes at each of these values, and to describe the manifolds at the regular values of energy, the homology groups of the integral manifolds are computed for the five energy regions on either side of the singular values. The homology group calculations establish that all four energy levels are indeed bifurcation values, and allows some of the global properties of the integral manifolds to be explored.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"48 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212575","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

Reducibility of Linear Quasi-periodic Hamiltonian Derivative Wave Equations and Half-Wave Equations Under the Brjuno Conditions 布儒诺条件下线性准周期哈密顿衍生波方程和半波方程的可重复性

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-08-29 DOI: 10.1007/s10884-024-10390-7

Zhaowei Lou

引用次数: 0

Geometric Structure of the Traveling Waves for 1D Degenerate Parabolic Equation 一维畸变抛物方程的行波几何结构

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-08-27 DOI: 10.1007/s10884-024-10389-0

Yu Ichida, Shoya Motonaga

{"title":"Geometric Structure of the Traveling Waves for 1D Degenerate Parabolic Equation","authors":"Yu Ichida, Shoya Motonaga","doi":"10.1007/s10884-024-10389-0","DOIUrl":"https://doi.org/10.1007/s10884-024-10389-0","url":null,"abstract":"We clarify the geometric structure of non-negative traveling waves for the spatial one-dimensional degenerate parabolic equation (U_{t}=U^{p}(U_{xx}+mu U)-delta U). This equation has a nonlinear term with a parameter (p>0) and the cases (0<p<1) and (p>1) have been investigated in the author’s previous studies. It has been pointed out that the classifications of the traveling waves for these two cases are not the same and thus a bifurcation phenomenon occurs at (p=1). However, the classification of the case (p=1) remains open since the conventional approaches do not work for this case, which have prevented us to understand how the traveling waves bifurcate. The difficulty for the case (p=1) is that the corresponding ordinary differential equation through the Poincaré compactification has the non-hyperbolic equilibrium at infinity and we need to estimate the asymptotic behaviors of the trajectories near it. In this paper, we solve this problem by using a new asymptotic approach, which is completely different from the asymptotic analysis performed in the previous studies, and clarify the structure of the traveling waves in the case of (p=1). We then discuss the rich structure of traveling waves of the equation from a geometric point of view.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"92 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212577","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

On Traveling Fronts of Combustion Equations in Spatially Periodic Media 论空间周期介质中燃烧方程的移动前沿

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-08-21 DOI: 10.1007/s10884-024-10388-1

Yasheng Lyu, Hongjun Guo, Zhi-Cheng Wang

引用次数: 0

Segregation Pattern in a Four-Component Reaction–Diffusion System with Mass Conservation 质量守恒的四组分反应-扩散系统中的分离模式

IF 1.3 4区数学

Journal of Dynamics and Differential Equations Pub Date : 2024-08-19 DOI: 10.1007/s10884-024-10387-2

Yoshihisa Morita, Yoshihito Oshita

{"title":"Segregation Pattern in a Four-Component Reaction–Diffusion System with Mass Conservation","authors":"Yoshihisa Morita, Yoshihito Oshita","doi":"10.1007/s10884-024-10387-2","DOIUrl":"https://doi.org/10.1007/s10884-024-10387-2","url":null,"abstract":"We deal with a four-component reaction–diffusion system with mass conservation in a bounded domain with the Neumann boundary condition. This system serves as a model describing the segregation pattern which emerges during the maintenance phase of asymmetric cell devision. By utilizing the mass conservation, the stationary problem of the system is reduced to a two-component elliptic system with nonlocal terms, formulated as the Euler–Lagrange equation of an energy functional. We first establish the spectral comparison theorem, relating the stability/instability of equilibrium solutions to the four-component system to that of the two-component system. This comparison follows from examining the eigenvalue problems of the linearized operators around equilibrium solutions. Subsequently, with an appropriate scaling, we prove a (Gamma )-convergence of the energy functional. Furthermore, in a cylindrical domain, we prove the existence of equilibrium solutions with monotone profile representing a segregation pattern. This is achieved by applying the gradient flow and the comparison principle to the reduced two-component system.","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"30 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212579","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