On the Global Existence of a Class of Strongly Coupled Parabolic Systems

2021/05/18 by Dung Le, Le, Dung
Engineering · Mathematics · #Stability and Controllability of Differential Equations #Nonlinear Partial Differential Equations #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2105.08615

Abstract

We establish the global existence of a class of strongly coupled parabolic systems. The necessary apriori estimates will be obtained via our new approach to the regularity theory of parabolic scalar equations with integrable data and new W^1,p estimates of their solutions. The key assumption here is that the L^p norms of solutions are uniformly bounded for some sufficiently large p∈ (1,∞), an assumption can be easily affirmed for systems with polynomial growth data. This replaces the usual condition that the solutions are uniformly bounded which is very hard to be verified because maximum principles for systems are generally unavailable.

Citations

• Parabolic Systems with Polynomial Growth and Regularity

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