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