Delayed blow-up and enhanced diffusion by transport noise for systems of reaction–diffusion equations

IF 1.4 3区数学 Q2 MATHEMATICS, APPLIED

Stochastics and Partial Differential Equations-Analysis and Computations Pub Date : 2023-11-28 DOI:10.1007/s40072-023-00319-4

Antonio Agresti

引用次数: 10

Abstract

This paper is concerned with the problem of regularization by noise of systems of reaction–diffusion equations with mass control. It is known that strong solutions to such systems of PDEs may blow-up in finite time. Moreover, for many systems of practical interest, establishing whether the blow-up occurs or not is an open question. Here we prove that a suitable multiplicative noise of transport type has a regularizing effect. More precisely, for both a sufficiently noise intensity and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary large time. Global existence is shown for the case of exponentially decreasing mass. The proofs combine and extend recent developments in regularization by noise and in the \(L^p(L^q)\)-approach to stochastic PDEs, highlighting new connections between the two areas.

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反应扩散方程系统的延迟爆破和输运噪声增强扩散

研究了具有质量控制的反应扩散方程系统的噪声正则化问题。已知这类偏微分方程系统的强解可能在有限时间内爆炸。此外，对于许多具有实际利益的系统来说，确定爆炸是否发生是一个悬而未决的问题。本文证明了适当的输运型乘性噪声具有正则化效应。更确切地说，对于足够的噪声强度和高频谱，强解的爆炸被延迟到任意大的时间。在质量呈指数递减的情况下，证明了整体存在性。这些证明结合并扩展了噪声正则化和\(L^p(L^q)\) -随机偏微分方程方法的最新发展，突出了这两个领域之间的新联系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Stochastics and Partial Differential Equations-Analysis and Computations Mathematics-Modeling and Simulation

CiteScore

2.70

自引率

13.30%

发文量

期刊介绍： Stochastics and Partial Differential Equations: Analysis and Computations publishes the highest quality articles presenting significantly new and important developments in the SPDE theory and applications. SPDE is an active interdisciplinary area at the crossroads of stochastic anaylsis, partial differential equations and scientific computing. Statistical physics, fluid dynamics, financial modeling, nonlinear filtering, super-processes, continuum physics and, recently, uncertainty quantification are important contributors to and major users of the theory and practice of SPDEs. The journal is promoting synergetic activities between the SPDE theory, applications, and related large scale computations. The journal also welcomes high quality articles in fields strongly connected to SPDE such as stochastic differential equations in infinite-dimensional state spaces or probabilistic approaches to solving deterministic PDEs.