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Existence and uniqueness of periodic solutions for a nonlinear reaction-diffusion problem.

Maurizio Badii (2000)

Publicacions Matemàtiques

We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.

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 and uniqueness of solutions for some degenerate nonlinear elliptic equations

Albo Carlos Cavalheiro (2014)

Archivum Mathematicum

In this article we are interested in the existence and uniqueness of solutions for the Dirichlet problem associated with the degenerate nonlinear elliptic equations Δ ( v ( x ) | Δ u | p - 2 Δ u ) - j = 1 n D j [ ω ( x ) 𝒜 j ( x , u , u ) ] = f 0 ( x ) - j = 1 n D j f j ( x ) , i n Ω in the setting of the weighted Sobolev spaces.

Existence and uniqueness of solutions of nonlinear infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (2001)

Annales Polonici Mathematici

We consider the Fourier first initial-boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations of parabolic type. The right-hand sides of the system are functionals of unknown functions. The existence and uniqueness of the solution are proved by the Banach fixed point theorem.

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