Integral conditions for uniqueness of solutions to degenerate parabolic equations

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:267

Article

Punzo, Fabio¹ 

[1] Politecn Milan, Dipartimento Matemat, Milan, Italy

关键词: Degenerate parabolic equations;    Uniqueness of solutions;    Unbounded solutions;   

DOI  :  10.1016/j.jde.2019.07.003

来源: Elsevier

【 摘 要 】

We investigate uniqueness of solutions to the initial value problem for degenerate parabolic equations, posed in bounded domains, where no boundary conditions are prescribed. In order to obtain uniqueness, we need that the solutions satisfy certain integral growth conditions, which are crucially related to the degeneracy of the operator near the boundary. In particular, such solutions can be unbounded near the boundary. Our hypothesis on the behavior of the operator at the boundary is optimal; in fact, we show that if it fails, then nonuniqueness of solutions prevails. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free