Journal of Differential Equations最新文献

{"title":"On the Benjamin-Bona-Mahony regularization of the Korteweg-de Vries equation","authors":"Younghun Hong ,&nbsp;Junyeong Jang ,&nbsp;Changhun Yang","doi":"10.1016/j.jde.2025.113626","DOIUrl":"10.1016/j.jde.2025.113626","url":null,"abstract":"<div><div>The Benjamin-Bona-Mahony equation (BBM) is introduced as a regularization of the Korteweg-de Vries equation (KdV) for long water waves [T.B. Benjamin, J.L. Bona, and J.J. Mahony, Philos. Trans. Roy. Soc. London Ser. A 272(1220) (1972), pp. 47–78]. In this paper, we establish the convergence from the BBM to the KdV for energy class solutions. As a consequence, employing the conservation laws, we extend the known temporal interval of validity for the BBM regularization.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"447 ","pages":"Article 113626"},"PeriodicalIF":2.4,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633368","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":"Non-uniqueness for the nonlinear dynamical Lamé system","authors":"Shunkai Mao ,&nbsp;Peng Qu","doi":"10.1016/j.jde.2025.113603","DOIUrl":"10.1016/j.jde.2025.113603","url":null,"abstract":"<div><div>We consider the Cauchy problem for the nonlinear dynamical Lamé system with double wave speeds in a <em>d</em>-dimensional <span><math><mo>(</mo><mi>d</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></span> periodic domain. Moreover, the equations can be transformed into a linearly degenerate hyperbolic system. We could construct infinitely many continuous solutions in <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>1</mn><mo>,</mo><mi>α</mi></mrow></msup></math></span> emanating from the same small initial data for <span><math><mi>α</mi><mo>&lt;</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>60</mn></mrow></mfrac></math></span>. The proof relies on the convex integration scheme. We construct a new class of building blocks with compression structure by using the double wave speeds characteristic of the equations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113603"},"PeriodicalIF":2.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632714","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":"On a weighted semilinear Steklov problem in exterior domains","authors":"Zongming Guo ,&nbsp;Fangshu Wan ,&nbsp;Dong Ye","doi":"10.1016/j.jde.2025.113608","DOIUrl":"10.1016/j.jde.2025.113608","url":null,"abstract":"<div><div>Let <em>B</em> be the unit ball in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup></math></span>, <span><math><mi>N</mi><mo>≥</mo><mn>3</mn></math></span>. We are interested in a weighted elliptic problem in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>﹨</mo><mover><mrow><mi>B</mi></mrow><mo>‾</mo></mover></math></span> with Steklov boundary conditions:<span><span><span>(0.1)</span><span><math><mrow><mo>{</mo><mtable><mtr><mtd><mo>−</mo><mtext>div</mtext><mo>(</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>θ</mi></mrow></msup><mi>∇</mi><mi>u</mi><mo>)</mo><mo>=</mo><mo>|</mo><mi>x</mi><msup><mrow><mo>|</mo></mrow><mrow><mi>ℓ</mi></mrow></msup><msup><mrow><mi>u</mi></mrow><mrow><mi>p</mi></mrow></msup><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mrow><mtext>in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>﹨</mo><mover><mrow><mi>B</mi></mrow><mo>‾</mo></mover></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mi>u</mi><mo>&gt;</mo><mn>0</mn><mspace></mspace></mtd><mtd><mrow><mtext>in </mtext><msup><mrow><mi>R</mi></mrow><mrow><mi>N</mi></mrow></msup><mo>﹨</mo><mover><mrow><mi>B</mi></mrow><mo>‾</mo></mover></mrow><mo>,</mo></mtd></mtr><mtr><mtd><mfrac><mrow><mo>∂</mo><mi>u</mi></mrow><mrow><mo>∂</mo><mi>ν</mi></mrow></mfrac><mo>+</mo><mi>d</mi><mi>u</mi><mo>=</mo><mn>0</mn><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace></mtd><mtd><mrow><mtext>on ∂</mtext><mtext>B</mtext></mrow><mo>,</mo></mtd></mtr></mtable></mrow></math></span></span></span> with <span><math><mi>d</mi><mo>∈</mo><mi>R</mi></math></span>, <span><math><mi>p</mi><mo>&gt;</mo><mn>1</mn></math></span> and<span><span><span>(0.2)</span><span><math><msup><mrow><mi>N</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>:</mo><mo>=</mo><mi>N</mi><mo>+</mo><mi>θ</mi><mo>&gt;</mo><mn>2</mn><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mspace></mspace><mi>τ</mi><mo>:</mo><mo>=</mo><mi>ℓ</mi><mo>−</mo><mi>θ</mi><mo>&gt;</mo><mo>−</mo><mn>2</mn><mo>.</mo></math></span></span></span> A complete picture of existence and nonexistence of radial solutions for <span><span>(0.1)</span></span> is obtained. Furthermore, for <span><math><mi>d</mi><mo>&lt;</mo><mn>0</mn></math></span>, the asymptotic behavior of radial solutions to <span><span>(0.1)</span></span> as <span><math><mi>p</mi><mo>→</mo><mo>∞</mo></math></span> is studied.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113608"},"PeriodicalIF":2.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632713","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":"Birkhoff center and statistical behavior of competitive dynamical systems","authors":"Xi Sheng ,&nbsp;Yi Wang ,&nbsp;Yufeng Zhang","doi":"10.1016/j.jde.2025.113623","DOIUrl":"10.1016/j.jde.2025.113623","url":null,"abstract":"<div><div>We investigate the location and structure of the Birkhoff center for competitive dynamical systems, and give a comprehensive description of recurrence and statistical behavior of orbits. An order-structure dichotomy is established for any connected component of the Birkhoff center, that is, either it is unordered, or it consists of strongly ordered equilibria. Moreover, there is a canonically defined countable disjoint family <span><math><mi>F</mi></math></span> of invariant <span><math><mo>(</mo><mi>n</mi><mo>−</mo><mn>1</mn><mo>)</mo></math></span>-cells such that each unordered connected component of the Birkhoff center lies on one of these cells. We further show that any connected component of the supports of invariant measures either consists of strongly ordered equilibria, or lies on one element of <span><math><mi>F</mi></math></span>. In particular, any 3-dimensional competitive flow has topological entropy 0.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113623"},"PeriodicalIF":2.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144632771","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":"Three closed characteristics on non-degenerate star-shaped hypersurfaces in R6","authors":"Huagui Duan ,&nbsp;Hui Liu ,&nbsp;Yiming Long ,&nbsp;Zihao Qi ,&nbsp;Wei Wang","doi":"10.1016/j.jde.2025.113605","DOIUrl":"10.1016/j.jde.2025.113605","url":null,"abstract":"<div><div>In this paper, we prove that for every non-degenerate <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> compact star-shaped hypersurface Σ in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>6</mn></mrow></msup></math></span> which carries no prime closed characteristic of Maslov-type index 0 or no prime closed characteristic of Maslov-type index −1, there exist at least three prime closed characteristics on Σ.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113605"},"PeriodicalIF":2.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631543","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":"Decay estimates for one Aharonov-Bohm solenoid in a uniform magnetic field II: Wave equation","authors":"Haoran Wang ,&nbsp;Fang Zhang ,&nbsp;Junyong Zhang","doi":"10.1016/j.jde.2025.113607","DOIUrl":"10.1016/j.jde.2025.113607","url":null,"abstract":"<div><div>This is the second paper of our project exploring the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In the first paper <span><span>[36]</span></span>, we have studied the dispersive and Strichartz estimates for the Schrödinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The decay estimate for the wave equation in the same setting turns out to be more delicate since the square root of the eigenvalue of the associated Schrödinger operator will prevent the direct construction of the half-wave propagator. To get around this obstacle, we turn to verify the Gaussian boundedness of the related heat kernel via two different approaches. The first one is based on the Davies-Gaffney inequality in this setting and the second one is to obtain an explicit representation of the heat kernel (which contains the full information of both the Aharonov-Bohm solenoid and the uniform magnetic field) with the aid of the Schulman-Sunada formula. As a byproduct, we also establish the Bernstein inequalities and the square function estimates for the involved Schrödinger operator with one Aharonov-Bohm solenoid in a uniform magnetic field.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113607"},"PeriodicalIF":2.4,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589048","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":"Diffusion approximation and stability of stochastic differential equations with singular perturbation","authors":"Huagui Liu ,&nbsp;Shujun Liu ,&nbsp;Fuke Wu ,&nbsp;Xiaofeng Zong","doi":"10.1016/j.jde.2025.113602","DOIUrl":"10.1016/j.jde.2025.113602","url":null,"abstract":"<div><div>This paper investigates diffusion approximation and stability of non-autonomous singularly perturbed stochastic differential equations with locally Lipschitz continuous coefficients. By using the first-order perturbation test function method and formulation of the martingale problem, the averaging principle is established and the averaging system is obtained. Under appropriate conditions, if the averaging system is exponentially stable, this paper shows that the original slow component is also uniformly asymptotically stable. Since the averaging system is often simpler than the original system, this stability result is interesting. Finally, several examples illustrate our results.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113602"},"PeriodicalIF":2.4,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589050","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":"Global bifurcation in symmetric systems of nonlinear wave equations","authors":"Carlos García-Azpeitia ,&nbsp;Ziad Ghanem ,&nbsp;Wiesław Krawcewicz","doi":"10.1016/j.jde.2025.113600","DOIUrl":"10.1016/j.jde.2025.113600","url":null,"abstract":"<div><div>In this paper, we use the equivariant degree theory to establish a global bifurcation result for the existence of non-stationary branches of solutions to a nonlinear, two-parameter family of hyperbolic wave equations with local delay and non-trivial damping. As a motivating example, we consider an application of our result to a system of <em>N</em> identical vibrating strings with dihedral coupling relations.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113600"},"PeriodicalIF":2.4,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144589049","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":"Sample path properties and small ball probabilities for stochastic fractional diffusion equations","authors":"Yuhui Guo ,&nbsp;Jian Song ,&nbsp;Ran Wang ,&nbsp;Yimin Xiao","doi":"10.1016/j.jde.2025.113604","DOIUrl":"10.1016/j.jde.2025.113604","url":null,"abstract":"<div><div>We consider the following stochastic space-time fractional diffusion equation with vanishing initial condition:<span><span><span><math><msup><mrow><mo>∂</mo></mrow><mrow><mi>β</mi></mrow></msup><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>−</mo><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>+</mo><msubsup><mrow><mi>I</mi></mrow><mrow><mn>0</mn><mo>+</mo></mrow><mrow><mi>γ</mi></mrow></msubsup><mrow><mo>[</mo><mover><mrow><mi>W</mi></mrow><mrow><mo>˙</mo></mrow></mover><mo>(</mo><mi>t</mi><mo>,</mo><mi>x</mi><mo>)</mo><mo>]</mo></mrow><mo>,</mo><mspace></mspace><mi>t</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo><mo>,</mo><mspace></mspace><mi>x</mi><mo>∈</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>d</mi></mrow></msup><mo>,</mo></math></span></span></span> where <span><math><mi>α</mi><mo>&gt;</mo><mn>0</mn></math></span>, <span><math><mi>β</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span>, <span><math><mi>γ</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>, <span><math><msup><mrow><mo>(</mo><mo>−</mo><mi>Δ</mi><mo>)</mo></mrow><mrow><mi>α</mi><mo>/</mo><mn>2</mn></mrow></msup></math></span> is the fractional/power of Laplacian and <span><math><mover><mrow><mi>W</mi></mrow><mrow><mo>˙</mo></mrow></mover></math></span> is a fractional space-time Gaussian noise. We prove the existence and uniqueness of the solution and then focus on various sample path regularity properties of the solution. More specifically, we establish the exact uniform and local moduli of continuity and Chung's laws of the iterated logarithm. The small ball probability is also studied.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113604"},"PeriodicalIF":2.4,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579418","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":"Inverse scattering problem for operators with a finite-dimensional non-local potential","authors":"V.A. Zolotarev","doi":"10.1016/j.jde.2025.113606","DOIUrl":"10.1016/j.jde.2025.113606","url":null,"abstract":"<div><div>Scattering problem for a self-adjoint integro-differential operator, which is the sum of the operator of the second derivative and of a finite-dimensional self-adjoint operator, is studied. Jost solutions are found and it is shown that the scattering function has a multiplicative structure, besides, each of the multipliers is a scattering coefficient for a pair of self-adjoint operators, one of which is a one-dimensional perturbation of the other. Solution of the inverse problem is based upon the solutions to the inverse problem for every multiplier. A technique for finding parameters of the finite-dimensional perturbation via the scattering data is described.</div></div>","PeriodicalId":15623,"journal":{"name":"Journal of Differential Equations","volume":"446 ","pages":"Article 113606"},"PeriodicalIF":2.4,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144579420","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}