Geodesic
Sufficient conditions on diffusivity for the existence and nonexistence of stable equilibria with nonlinear flux on the boundary
Electronic journal of differential equations, Tome 2012 (2012)
A reaction-diffusion equation with variable diffusivity and nonlinear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.
Classification : 35J25, 35B35, 35B36
Keywords: reaction-diffusion equation, stable stationary solutions, variable diffusivity, implicit function theorem 
@article{EJDE_2012__2012__a41,
     author = {Crema,  Janete and Do Nascimento,  Arnaldo Simal and Sonego,  Maicon},
     title = {Sufficient conditions on diffusivity for the existence and nonexistence of stable equilibria with nonlinear flux on the boundary},
     journal = {Electronic journal of differential equations},
     year = {2012},
     volume = {2012},
     zbl = {1238.35044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a41/}
}
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JO  - Electronic journal of differential equations
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%A Sonego,  Maicon
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%J Electronic journal of differential equations
%D 2012
%V 2012
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%G en
%F EJDE_2012__2012__a41
Crema,  Janete; Do Nascimento,  Arnaldo Simal; Sonego,  Maicon. Sufficient conditions on diffusivity for the existence and nonexistence of stable equilibria with nonlinear flux on the boundary. Electronic journal of differential equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a41/