Geodesic
Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35K05, 35K10, 35K20, 35K58, 35K65
Keywords: initial boundary value problems, Galerkin approximations, energy estimates, Banach fixed point theorem, existence and uniqueness of weak solutions 
@article{EJDE_2014__2014__a7,
     author = {Sanni,  Sikiru Adigun},
     title = {Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1297.35120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a7/}
}
TY  - JOUR
AU  - Sanni,  Sikiru Adigun
TI  - Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term
JO  - Electronic journal of differential equations
PY  - 2014
VL  - 2014
UR  - http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a7/
LA  - en
ID  - EJDE_2014__2014__a7
ER  - 
%0 Journal Article
%A Sanni,  Sikiru Adigun
%T Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term
%J Electronic journal of differential equations
%D 2014
%V 2014
%U http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a7/
%G en
%F EJDE_2014__2014__a7
Sanni,  Sikiru Adigun. Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a7/