Nonlinear Convection in Reaction-diffusion Equations under dynamical boundary conditions

Details Nonlinear Convection in Reaction-diffusion Equations under dynamical boundary conditions Nonlinear Convection in Reaction-diffusion Equations under dynamical boundary conditions

2012-02-10

arxiv.org/abs/1202.2220v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

We investigate blow-up phenomena for positive solutions of nonlinear reaction-diffusion equations including a nonlinear convection term $\partial_t u = \Delta u - g(u) \cdot \nabla u + f(u)$ in a bounded domain of $\mathbb{R}^N$ under the dissipative dynamical boundary conditions $\sigma \partial_t u + \partial_\nu u =0$. 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.

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