Geodesic
Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term
Electronic Journal of Differential Equations, Tome 2014 (2014).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a107,
     author = {Sanni, Sikiru Adigun},
     title = {Nonlocal degenerate reaction-diffusion equations with general nonlinear diffusion term},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2014},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a107/}
}
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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__a107/