Blow-up phenomena for a class of nonlinear reaction-diffusion equations under nonlinear boundary conditions. Issue 16 (10th December 2019)

• Record Type: Journal Article
• Authors: Zhang, Ling-Ling; Tian, Hui-Min
• Is Part Of: Applicable analysis. Volume 98:Issue 16(2019)
• Page Start: 2868
• Page End: 2883
• Publication Date: 2019-12-10
• Subjects: Reaction-diffusion equations -- blow-up -- lower and upper bounds; 35K57 -- 35K55 -- 35K10; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2018.1478079
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: The paper considers the blow-up solution for the following nonlinear reaction-diffusion equations under nonlinear boundary conditions: ( h ( u ) ) t = ∇ ⋅ ( ρ ( | ∇ u | p ) | ∇ u | p − 2 ∇ u ) + b ( x ) k ( t ) f ( u ), ( x, t ) ∈ Ω × ( 0, T ), ρ ( | ∇ u | p ) | ∇ u | p − 2 ∂ u ∂ n = g ( u ), ( x, t ) ∈ ∂Ω × ( 0, T ), u ( x, 0 ) = u 0 ( x ) ≥ 0, x ∈ Ω ¯, where p >2 and Ω ⊂ R N ( N > 2 ) is a bounded convex domain with smooth boundary ∂Ω . By means of constructing auxiliary functions and a first-order differential inequality technique, we obtain the upper and lower bounds on blow-up time under some appropriate assumptions. Moreover, some examples are also presented as application of our main results.