Geodesic
Existence of positive solutions for some nonlinear parabolic equations in the half space
Electronic Journal of Differential Equations, Tome 2010 (2010).

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

Summary: We prove the existence of positive solutions to the nonlinear parabolic equation $$ \Delta u - \frac{\partial u}{\partial t}=p(x,t)f(u) $$ in the half space $\mathbb{R}^n_{+}, n\geq 2$, subject to Dirichlet boundary conditions. The function f is nonnegative continuous non-increasing, and the potential p is nonnegative and satisfies some hypotheses related to the parabolic Kato class. We use potential theory arguments to prove our main result.
Classification : 35J55, 35J60, 35J65
Keywords: parabolic Kato class, parabolic equation, positive solutions 
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     author = {Ghanmi, Abdeljabbar},
     title = {Existence of positive solutions for some nonlinear parabolic equations in the half space},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a185/}
}
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Ghanmi, Abdeljabbar. Existence of positive solutions for some nonlinear parabolic equations in the half space. Electronic Journal of Differential Equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a185/