当前位置: X-MOL 学术Discrete Contin. Dyn. Syst. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Existence of solution for a class of heat equation in whole $ \mathbb{R}^N $
Discrete and Continuous Dynamical Systems ( IF 1.1 ) Pub Date : 2021-02-07 , DOI: 10.3934/dcds.2021031
Claudianor O. Alves , , Tahir Boudjeriou ,

In this paper we study the local and global existence of solutions for a class of heat equation in whole $ \mathbb{R}^{N} $ where the nonlinearity has a critical growth for $ N \geq 2 $. In order to prove the global existence, we will use the potential well theory combined with the Nehari manifold, and also with the Pohozaev manifold that is a novelty for this type of problem. Moreover, the blow-up phenomena of local solutions is investigated by combining the subdifferential approach with the concavity method.

中文翻译:

一元热方程在整体$ \ mathbb {R} ^ N $中的解的存在性

在本文中,我们研究了整体$ \ mathbb {R} ^ {N} $中一类热方程解的局部和全局存在性,其中非线性对于$ N \ geq 2 $具有临界增长。为了证明整体存在,我们将使用势阱理论与Nehari流形以及Pohozaev流形相结合,这是此类问题的新颖之处。此外,通过将亚微分方法与凹面方法相结合,研究了局部解的爆炸现象。
更新日期:2021-02-07
down
wechat
bug