Electron. J. Diff. Equ.,
Vol. 2014 (2014), No. 124, pp. 127.
Nonlocal degenerate reactiondiffusion equations with
general nonlinear diffusion term
Sikiru Adigun Sanni
Abstract:
We study a class of secondorder nonlocal degenerate semilinear
reactiondiffusion 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 blowup 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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