论文标题
反应扩散方程系统的传输噪声延迟爆破和增强的扩散
Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion equations
论文作者
论文摘要
本文涉及通过质量控制的反应扩散方程系统的噪声正规化问题。众所周知，$ \ textit {strong} $解决方案对此类PDE系统可能会在有限的时间内爆炸。此外，对于许多实践感兴趣的系统，确定爆炸是否发生是一个悬而未决的问题。在这里，我们证明了合适的运输类型乘法噪声具有正则效果。更确切地说，对于足够的噪声强度和频谱，强溶液的爆炸被延迟，并且还建立了增强的扩散效果。显示了质量下降质量的情况。这些证据结合了噪声和$ l^p（l^q）$的正规化方面的最新发展 - 随机PDE的方法，突出了两个区域之间的新连接。
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ 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 sufficiently noise intensity and spectrum, the blow-up of strong solutions is delayed and an enhanced diffusion effect is also established. 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.
