Blow-Up Phenomena for Nonlinear Reaction-Diffusion Equations under Nonlinear Boundary Conditions. (20th March 2016)

• Record Type: Journal Article
• Authors: Ding, Juntang
• Other Names: Olszowy Leszek Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2016(2016)
• Publication Date: 2016-03-20
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2016/8107657
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : This paper deals with blow-up and global solutions of the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: g ( u ) t = ∇ · a u ∇ u + f u in Ω × 0, T, ∂ u / ∂ n = b x, u, t on ∂ Ω × ( 0, T ), u ( x, 0 ) = u 0 ( x ) > 0, in Ω ¯, where Ω ⊂ R N ( N ≥ 2 ) is a bounded domain with smooth boundary ∂ Ω . We obtain the conditions under which the solutions either exist globally or blow up in a finite time by constructing auxiliary functions and using maximum principles. Moreover, the upper estimates of the "blow-up time, " the "blow-up rate, " and the global solutions are also given.