Pub Date : 2025-12-19DOI: 10.1016/j.na.2025.114042
Flank D.M. Bezerra , Vando Narciso , Senlin Yan
This paper is dedicated to the analysis of the pullback dynamics of a non-autonomous Balakrishnan-Taylor beam with a strong damping dependent on the time and linear energy of the system. In the main result we establish the existence of a pullback attractor for the evolution process generated by the weak solutions of the system. In addition, we also prove a result of upper semicontiunity of attractors with respect to functional parameters present in the damped term.
{"title":"Pullback dynamics for a class of plate equations with time-dependent energy damping","authors":"Flank D.M. Bezerra , Vando Narciso , Senlin Yan","doi":"10.1016/j.na.2025.114042","DOIUrl":"10.1016/j.na.2025.114042","url":null,"abstract":"<div><div>This paper is dedicated to the analysis of the pullback dynamics of a non-autonomous Balakrishnan-Taylor beam with a strong damping dependent on the time and linear energy of the system. In the main result we establish the existence of a pullback attractor for the evolution process generated by the weak solutions of the system. In addition, we also prove a result of upper semicontiunity of attractors with respect to functional parameters present in the damped term.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114042"},"PeriodicalIF":1.3,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797902","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}
Pub Date : 2025-12-18DOI: 10.1016/j.na.2025.114040
Tianlan Chen , Christopher S. Goodrich
We consider a class of nonlocal elliptic PDEs, of which one model case is the steady-state Kirchhoff-type equationwhere is the unit ball in , where n ≥ 2. Under the assumption that u satisfies Dirichlet boundary datum on , we demonstrate existence of at least one positive radially symmetric solution to the PDE by means of topological fixed point theory. Our results are valid both in the low-dimensional setting (n < p) and the high-dimensional setting (n ≥ p), though the techniques required differ between the two cases. The existence arguments utilise a specialised order cone.
{"title":"Radially symmetric solutions of nonlocal elliptic equations on the unit ball","authors":"Tianlan Chen , Christopher S. Goodrich","doi":"10.1016/j.na.2025.114040","DOIUrl":"10.1016/j.na.2025.114040","url":null,"abstract":"<div><div>We consider a class of nonlocal elliptic PDEs, of which one model case is the steady-state Kirchhoff-type equation<span><span><span><math><mrow><mo>−</mo><msubsup><mrow><mi>M</mi><mo>(</mo><mo>∥</mo><mi>D</mi><mi>u</mi><mo>∥</mo></mrow><mrow><msup><mi>L</mi><mi>p</mi></msup></mrow><mi>p</mi></msubsup><mo>)</mo><mstyle><mi>Δ</mi></mstyle><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><mi>λ</mi><mi>f</mi><mo>(</mo><mrow><mo>|</mo><mi>x</mi><mo>|</mo></mrow><mo>,</mo><mi>u</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>)</mo><mtext>,</mtext><mspace></mspace><mi>x</mi><mo>∈</mo><msub><mi>B</mi><mn>1</mn></msub><mo>,</mo></mrow></math></span></span></span>where <span><math><msub><mi>B</mi><mn>1</mn></msub></math></span> is the unit ball in <span><math><msup><mi>R</mi><mi>n</mi></msup></math></span>, where <em>n</em> ≥ 2. Under the assumption that <em>u</em> satisfies Dirichlet boundary datum on <span><math><mrow><mi>∂</mi><msub><mi>B</mi><mn>1</mn></msub></mrow></math></span>, we demonstrate existence of at least one positive radially symmetric solution to the PDE by means of topological fixed point theory. Our results are valid both in the low-dimensional setting (<em>n</em> < <em>p</em>) and the high-dimensional setting (<em>n</em> ≥ <em>p</em>), though the techniques required differ between the two cases. The existence arguments utilise a specialised order cone.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114040"},"PeriodicalIF":1.3,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797901","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}
Pub Date : 2025-12-16DOI: 10.1016/j.na.2025.114032
Yan Zhuang , Yanmin Niu , Daxiong Piao
In this paper, we obtain the invariant curves of quasi-periodic reversible mappings with finite s-smoothness. Since the reversible property is difficult to maintain in the process of approximating smooth functions by analytical ones, Rüssmann’s classical method in reduction of smoothness [1] cannot be directly applied since it does not preserve the reversible property. Inspired by the fact that a reversible mapping can be regarded as the Poincaré map of a reversible differential equation, we establish a new KAM theorem for a reversible differential equation which is quasi-periodic in angle variable, and then obtain the invariant curves of the reversible mapping. Beyond that, we prove some variants of invariant curve theorems for quasi-periodic reversible mappings. As an application, the boundedness of solutions for a class of semilinear oscillator is discussed by the obtained results at last.
{"title":"Invariant curves of low smooth quasi-periodic reversible mappings","authors":"Yan Zhuang , Yanmin Niu , Daxiong Piao","doi":"10.1016/j.na.2025.114032","DOIUrl":"10.1016/j.na.2025.114032","url":null,"abstract":"<div><div>In this paper, we obtain the invariant curves of quasi-periodic reversible mappings with finite s-smoothness. Since the reversible property is difficult to maintain in the process of approximating smooth functions by analytical ones, Rüssmann’s classical method in reduction of smoothness [1] cannot be directly applied since it does not preserve the reversible property. Inspired by the fact that a reversible mapping can be regarded as the Poincaré map of a reversible differential equation, we establish a new KAM theorem for a reversible differential equation which is quasi-periodic in angle variable, and then obtain the invariant curves of the reversible mapping. Beyond that, we prove some variants of invariant curve theorems for quasi-periodic reversible mappings. As an application, the boundedness of solutions for a class of semilinear oscillator is discussed by the obtained results at last.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114032"},"PeriodicalIF":1.3,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797904","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}
Pub Date : 2025-12-16DOI: 10.1016/j.na.2025.114035
Patrick Maheux , Vittoria Pierfelice
In this paper, we revisit the blow-up criteria for the simplest parabolic-elliptic Patlak-Keller-Segel (PKS) system in the 2D Euclidean space, including a consumption term. In the supercritical mass case M > 8π, and under an additional global assumption on the second moment (or variance) of the initial data, we establish blow-up results for a broader class of initial conditions than those traditionally considered. We also derive improved upper bounds for the maximal existence time of (PKS) solutions on the plane. These time estimates are obtained through a sharp analysis of a one-parameter differential inequality governing the evolution of the second moment of the (PKS) system.
In particular, we obtain that for any n0 with finite second order moment, λn0 for λ sufficiently large provide an initial datum yielding blow up. The current blow up criterion is also compared to the available ones in the literature.
{"title":"Revisiting the blow-up criterion and the maximal existence time for solutions of the parabolic-Elliptic keller-Segel system in 2D-euclidean space","authors":"Patrick Maheux , Vittoria Pierfelice","doi":"10.1016/j.na.2025.114035","DOIUrl":"10.1016/j.na.2025.114035","url":null,"abstract":"<div><div>In this paper, we revisit the blow-up criteria for the simplest parabolic-elliptic Patlak-Keller-Segel (PKS) system in the 2D Euclidean space, including a consumption term. In the supercritical mass case <em>M</em> > 8<em>π</em>, and under an additional global assumption on the second moment (or variance) of the initial data, we establish blow-up results for a broader class of initial conditions than those traditionally considered. We also derive improved upper bounds for the maximal existence time of (PKS) solutions on the plane. These time estimates are obtained through a sharp analysis of a one-parameter differential inequality governing the evolution of the second moment of the (PKS) system.</div><div>In particular, we obtain that for any <em>n</em><sub>0</sub> with finite second order moment, <em>λn</em><sub>0</sub> for <em>λ</em> sufficiently large provide an initial datum yielding blow up. The current blow up criterion is also compared to the available ones in the literature.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114035"},"PeriodicalIF":1.3,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797906","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}
Pub Date : 2025-12-16DOI: 10.1016/j.na.2025.114038
Vitor Gusson , Claudio Pessoa , Lucas Queiroz
In this work, we study isochronous centers on center manifolds of three-dimensional systems of differential equations. We describe in detail an algorithm that provides the necessary conditions for a Hopf point, when it is a center, to be isochronous, without initially requiring the system to be restricted to an explicit expression of the center manifold or a finite power series expansion of this expression. In addition, we determine necessary and sufficient conditions for a center on the center manifold of certain classes of quadratic three-dimensional systems of differential equations to be isochronous. The algorithm has an algebraic nature, inspired by a counterpart developed for the two-dimensional case, and offers lower computational cost in obtaining the isochronicity conditions.
{"title":"Isochronous centers on center manifolds in R3","authors":"Vitor Gusson , Claudio Pessoa , Lucas Queiroz","doi":"10.1016/j.na.2025.114038","DOIUrl":"10.1016/j.na.2025.114038","url":null,"abstract":"<div><div>In this work, we study isochronous centers on center manifolds of three-dimensional systems of differential equations. We describe in detail an algorithm that provides the necessary conditions for a Hopf point, when it is a center, to be isochronous, without initially requiring the system to be restricted to an explicit expression of the center manifold or a finite power series expansion of this expression. In addition, we determine necessary and sufficient conditions for a center on the center manifold of certain classes of quadratic three-dimensional systems of differential equations to be isochronous. The algorithm has an algebraic nature, inspired by a counterpart developed for the two-dimensional case, and offers lower computational cost in obtaining the isochronicity conditions.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114038"},"PeriodicalIF":1.3,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797905","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}
Pub Date : 2025-12-16DOI: 10.1016/j.na.2025.114036
Sitao Zhang
Based on the concept of mixed LYZ ellipsoid and the technique of isotropic embedding, a sharp reverse affine isoperimetric inequality is established in this paper. This inequality is a generalization of a weak version of the Mahler conjecture obtained by Lutwak, Yang, and Zhang [31].
{"title":"A sharp volume inequality for mixed LYZ ellipsoids","authors":"Sitao Zhang","doi":"10.1016/j.na.2025.114036","DOIUrl":"10.1016/j.na.2025.114036","url":null,"abstract":"<div><div>Based on the concept of mixed LYZ ellipsoid and the technique of isotropic embedding, a sharp reverse affine isoperimetric inequality is established in this paper. This inequality is a generalization of a weak version of the Mahler conjecture obtained by Lutwak, Yang, and Zhang [31].</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114036"},"PeriodicalIF":1.3,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145798491","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}
Pub Date : 2025-12-09DOI: 10.1016/j.na.2025.114028
Animesh Biswas , Mikil D. Foss , Petronela Radu
In this paper we introduce and study the concept of nonlocal ordered curvature. In the classical (differential) setting, the problem was introduced by Li and Nirenberg in [1, 2] where they conjectured (and proved in some cases) that if a bounded smooth surface has its mean curvature ordered in a particular direction, then the surface must be symmetric with respect to some hyperplane orthogonal to that direction. The conjecture was finally settled by Li et al in 2021 [3]. Here we study the counterpart problem in the nonlocal setting, where the nonlocal mean curvature of a set Ω, at any point x on its boundary, is defined as and the kernel function J is radially symmetric, non-increasing, integrable and compactly supported. Using a generalization of Alexandrov’s moving plane method, we prove a similar result in the nonlocal setting.
{"title":"Nonlocal ordered mean curvature with integrable kernels","authors":"Animesh Biswas , Mikil D. Foss , Petronela Radu","doi":"10.1016/j.na.2025.114028","DOIUrl":"10.1016/j.na.2025.114028","url":null,"abstract":"<div><div>In this paper we introduce and study the concept of nonlocal ordered curvature. In the classical (differential) setting, the problem was introduced by Li and Nirenberg in [1, 2] where they conjectured (and proved in some cases) that if a bounded smooth surface has its mean curvature ordered in a particular direction, then the surface must be symmetric with respect to some hyperplane orthogonal to that direction. The conjecture was finally settled by Li et al in 2021 [3]. Here we study the counterpart problem in the nonlocal setting, where the nonlocal mean curvature of a set Ω, at any point <em>x</em> on its boundary, is defined as <span><math><mrow><msubsup><mi>H</mi><mstyle><mi>Ω</mi></mstyle><mi>J</mi></msubsup><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mo>∫</mo><msup><mstyle><mi>Ω</mi></mstyle><mi>c</mi></msup></msub><mi>J</mi><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>d</mi><mi>y</mi><mo>−</mo><msub><mo>∫</mo><mstyle><mi>Ω</mi></mstyle></msub><mi>J</mi><mrow><mo>(</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>)</mo></mrow><mi>d</mi><mi>y</mi></mrow></math></span> and the kernel function <em>J</em> is radially symmetric, non-increasing, integrable and compactly supported. Using a generalization of Alexandrov’s moving plane method, we prove a similar result in the nonlocal setting.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114028"},"PeriodicalIF":1.3,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749108","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}
Pub Date : 2025-12-05DOI: 10.1016/j.na.2025.114031
Hao Chen , Yongkai Liao , Ling Wan
We study global-in-time spherically symmetric solutions for a viscous, compressible, heat-conducting ionized gas in a n-dimensional unbounded exterior domain with large initial data, where n ≥ 2 is the space dimension. The properties of ionized gases, combined with the unboundedness of the exterior domain, make it challenging to estimate the first-order spatial derivatives of the bulk velocity and the absolute temperature. For a class of constant non-vacuum equilibrium states, we obtain the uniform-in-time bounds on the dissipative estimates for both the bulk velocity and the absolute temperature. Based on such estimates, we establish the global existence and asymptotic behavior of spherically symmetric solutions to the viscous and heat-conducting ionized gas in unbounded exterior domains with large initial data. The key point lies in deducing the lower and upper bounds on the specific volume and the temperature.
{"title":"Global existence and large-time behavior of spherically symmetric solutions for a viscous heat-conducting ionized gas in exterior domains","authors":"Hao Chen , Yongkai Liao , Ling Wan","doi":"10.1016/j.na.2025.114031","DOIUrl":"10.1016/j.na.2025.114031","url":null,"abstract":"<div><div>We study global-in-time spherically symmetric solutions for a viscous, compressible, heat-conducting ionized gas in a <em>n</em>-dimensional unbounded exterior domain with large initial data, where <em>n</em> ≥ 2 is the space dimension. The properties of ionized gases, combined with the unboundedness of the exterior domain, make it challenging to estimate the first-order spatial derivatives of the bulk velocity and the absolute temperature. For a class of constant non-vacuum equilibrium states, we obtain the uniform-in-time bounds on the dissipative estimates for both the bulk velocity and the absolute temperature. Based on such estimates, we establish the global existence and asymptotic behavior of spherically symmetric solutions to the viscous and heat-conducting ionized gas in unbounded exterior domains with large initial data. The key point lies in deducing the lower and upper bounds on the specific volume and the temperature.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114031"},"PeriodicalIF":1.3,"publicationDate":"2025-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694789","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}
Pub Date : 2025-12-04DOI: 10.1016/j.na.2025.114029
Francesco Nobili, Ivan Yuri Violo
We study the generalized existence of extremizers for the sharp p-Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean volume growth assumptions. Assuming a nonnegative Ricci curvature lower bound, we show that almost extremal functions are close in gradient norm to radial Euclidean bubbles. In the case of nonnegative sectional curvature lower bounds, we additionally deduce that vanishing is the only possible behavior, in the sense that almost extremal functions are almost zero globally. Our arguments rely on nonsmooth concentration compactness methods and Mosco-convergence results for the Cheeger energy on noncompact varying spaces, generalized to every exponent p ∈ (1, ∞).
{"title":"Generalized existence of extremizers for the sharp p-Sobolev inequality on Riemannian manifolds with nonnegative curvature","authors":"Francesco Nobili, Ivan Yuri Violo","doi":"10.1016/j.na.2025.114029","DOIUrl":"10.1016/j.na.2025.114029","url":null,"abstract":"<div><div>We study the generalized existence of extremizers for the sharp <em>p</em>-Sobolev inequality on noncompact Riemannian manifolds in connection with nonnegative curvature and Euclidean volume growth assumptions. Assuming a nonnegative Ricci curvature lower bound, we show that almost extremal functions are close in gradient norm to radial Euclidean bubbles. In the case of nonnegative sectional curvature lower bounds, we additionally deduce that vanishing is the only possible behavior, in the sense that almost extremal functions are almost zero globally. Our arguments rely on nonsmooth concentration compactness methods and Mosco-convergence results for the Cheeger energy on noncompact varying spaces, generalized to every exponent <em>p</em> ∈ (1, ∞).</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114029"},"PeriodicalIF":1.3,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145694793","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}
Pub Date : 2025-12-03DOI: 10.1016/j.na.2025.114019
Ilia Naumkin
We investigate a stochastic nonlinear Schrödinger equation (NSE) posed on a multidimensional hyperoctant, where randomness enters both the domain interior and the boundary. The model incorporates additive interior noise and time-dependent stochastic Dirichlet boundary conditions, making it a prototypical system for analyzing the interplay between bulk stochasticity and boundary-driven randomness. We establish well-posedness by first developing a linear deterministic framework using Laplace and Riemann-Hilbert transform techniques, adapted to nonhomogeneous boundary data. The stochastic structure is then rigorously handled via fixed-point arguments in suitable function spaces, accounting for both cylindrical Wiener processes and stochastic convolutions. The solution is represented explicitly in terms of deterministic and stochastic Green operators, with an additional boundary evolution term that captures the diffusion of noise from the boundary into the domain. Our results provide conditions for existence, uniqueness, and regularity of mild solutions, and highlight how boundary noise can influence solution behavior through resonance, instability, or enhanced dispersion effects. This work contributes to the mathematical understanding of boundary-sensitive stochastic dispersive systems and lays a foundation for future analysis of noise-induced phenomena in high-dimensional domains.
{"title":"Stochastic forcing in nonlinear dispersive systems: Interior–boundary noise interactions on hyperoctants","authors":"Ilia Naumkin","doi":"10.1016/j.na.2025.114019","DOIUrl":"10.1016/j.na.2025.114019","url":null,"abstract":"<div><div>We investigate a stochastic nonlinear Schrödinger equation (NSE) posed on a multidimensional hyperoctant, where randomness enters both the domain interior and the boundary. The model incorporates additive interior noise and time-dependent stochastic Dirichlet boundary conditions, making it a prototypical system for analyzing the interplay between bulk stochasticity and boundary-driven randomness. We establish well-posedness by first developing a linear deterministic framework using Laplace and Riemann-Hilbert transform techniques, adapted to nonhomogeneous boundary data. The stochastic structure is then rigorously handled via fixed-point arguments in suitable function spaces, accounting for both cylindrical Wiener processes and stochastic convolutions. The solution is represented explicitly in terms of deterministic and stochastic Green operators, with an additional boundary evolution term that captures the diffusion of noise from the boundary into the domain. Our results provide conditions for existence, uniqueness, and regularity of mild solutions, and highlight how boundary noise can influence solution behavior through resonance, instability, or enhanced dispersion effects. This work contributes to the mathematical understanding of boundary-sensitive stochastic dispersive systems and lays a foundation for future analysis of noise-induced phenomena in high-dimensional domains.</div></div>","PeriodicalId":49749,"journal":{"name":"Nonlinear Analysis-Theory Methods & Applications","volume":"266 ","pages":"Article 114019"},"PeriodicalIF":1.3,"publicationDate":"2025-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145659107","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}
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