Nonlinear Convection in Reaction-diffusion Equations under dynamical boundary conditions

2012/02/10 by Gaëlle Pincet Mailly, Mailly, Gaëlle Pincet, Jean-François Rault +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1202.2220

20 pages

arxiv created 2012/09/25 · arxiv updated 2012/09/26

Abstract

We investigate blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term ∂_t u = Δu - g(u) ⋅ ∇ u + f(u) in a bounded domain of ℝ^N under the dissipative dynamical boundary conditions σ∂_t u + ∂_νu =0. Some conditions on g and f are discussed to state if the positive solutions blow up in finite time or not. Moreover, for certain classes of nonlinearities, an upper-bound for the blow-up time can be derived and the blow-up rate can be determinated.

Cited by

• Boundary Stabilization of Quasilinear Parabolic PDEs that Blow Up in Open Loop for Arbitrarily Small Initial Conditions

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