Agresti Antonio
Institute of Science and Technology Austria (ISTA), Am Campus 1, 3400 Klosterneuburg, Austria.
Present Address: Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands.
Stoch Partial Differ Equ. 2024;12(3):1907-1981. doi: 10.1007/s40072-023-00319-4. Epub 2023 Nov 28.
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that 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 -approach to stochastic PDEs, highlighting new connections between the two areas.
本文关注具有质量控制的反应扩散方程组的噪声正则化问题。已知此类偏微分方程组的解可能在有限时间内爆破。此外，对于许多具有实际意义的系统，确定爆破是否发生是一个悬而未决的问题。在此我们证明，一种合适的输运型乘性噪声具有正则化作用。更确切地说，对于足够大的噪声强度和高频谱，强解的爆破会延迟到任意长的时间。对于质量呈指数衰减的情况，证明了全局存在性。证明过程结合并扩展了噪声正则化以及随机偏微分方程的(L^p)方法方面的最新进展，突出了这两个领域之间的新联系。
