Electron. J. Diff. Equ., Vol. 2014 (2014), No. 124, pp. 1-27.

Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term

Sikiru Adigun Sanni

We study a class of second-order nonlocal degenerate semilinear reaction-diffusion equations with general nonlinear diffusion term. Under a set of conditions on the general nonlinear diffusivity and nonlinear nonlocal source term, we prove global existence and uniqueness results in a subset of a Sobolev space. Furthermore, we prove nonexistence of smooth solution or blow-up of solution under some other set of conditions. Lastly, we give illustrative examples for which our results apply.

Submitted February 5, 2014. Published May 14, 2014.
Math Subject Classifications: 35K05, 35K10, 35K20, 35K58, 35K65.
Key Words: Initial boundary value problems; Galerkin approximations; energy estimates; Banach fixed point theorem; existence and uniqueness of weak solutions.

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Sikiru Adigun Sanni
Department of Mathematics & Statistics
University of Uyo, Uyo 520003, Nigeria
email: sikirusanni@yahoo.com

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