Author:
Li Yuanfei,Guo Lianhong,Zeng Peng
Abstract
AbstractThe aim of this paper is to show some applications of Sobolev inequalities in partial differential equations. With the aid of some well-known inequalities, we derive the existence of global solution for the quasilinear parabolic equations. When the blow-up occurs, we derive the lower bound of the blow-up solution.
Funder
Foundation for natural Science in Higher Education of Guangdong
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference21 articles.
1. Bandle, C.: Isoperimetric Inequalities and Their Applications. Pitman, London (1980)
2. Bebernes, J., Eberly, D.: Mathematical Problems from Combustion Theory. Springer, New York (1989)
3. Biswas, I., Majee, A., Vallet, G.: On the Cauchy problem of a degenerate parabolic-hyperbolic PDE with Lévy noise. Adv. Nonlinear Anal. 8(1), 809–844 (2019)
4. Brezis, H.: Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer, New York (2011)
5. Chen, C.S., Huang, J.C.: Some nonexistence results for degenerate parabolic inequalities with local and nonlocal nonlinear terms. J. Nanjing Univ. Math. Biq. 21(1), 12–20 (2004)
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