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Existence and uniqueness of solutions for a degenerate quasilinear parabolic problem.

Maurizio Badii (1994)

Publicacions Matemàtiques

We consider the following quasilinear parabolic equation of degenerate type with convection term ut = φ (u)xx + b(u)x in (-L,0) x (0,T). We solve the associate initial-boundary data problem, with nonlinear flux conditions. This problem describes the evaporation of an incompressible fluid from a homogeneous porous media. The nonlinear condition in x = 0 means that the flow of fluid leaving the porous media depends on variable meteorological conditions and in a nonlinear manner on u. In x = -L we...

Existence et unicité de la solution pour un système de deux E.D.P.

Lahcen Ghannam (1989)

Publicacions Matemàtiques

We give some results on the existence, uniqueness and regularity of a nonlinear evolution system. This system models the viscoelastic behaviour of unicellular marine alga Acetabularia mediterrania when the calcium concentration varies. We show (with the aid of a fixed-point theorem) that the system admits a unique local solution in time.

Existence of periodic solutions for semilinear parabolic equations

Norimichi Hirano, Noriko Mizoguchi (1996)

Banach Center Publications

In this paper, we are concerned with the semilinear parabolic equation ∂u/∂t - Δu = g(t,x,u) if ( t , x ) R + × Ω u = 0 if ( t , x ) R + × Ω , where Ω R N is a bounded domain with smooth boundary ∂Ω and g : R + × Ω ¯ × R R is T-periodic with respect to the first variable. The existence and the multiplicity of T-periodic solutions for this problem are shown when g(t,x,ξ)/ξ lies between two higher eigenvalues of - Δ in Ω with the Dirichlet boundary condition as ξ → ±∞.

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