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