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We consider a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in $ℝ^{N}$ . Using a revised version of Bernstein’s method we provide several uniform estimates for the semigroup ${T (t)}_{t \geq 0}$ associated with the realization of the operator $𝒜$ in the space of all the bounded and continuous functions in $ℝ^{N}$

Exact solutions to some nonlinear PDEs, travelling profiles method.

Benhamidouche, N. (2008)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence and attractivity results for a class of degenerate functional-parabolic problems

M. Badii, J. I. Diaz, A. Tesei (1987)

Rendiconti del Seminario Matematico della Università di Padova

Existence and attractors of solutions for nonlinear parabolic systems.

El Hachimi, A., El Quardi, H. (2001)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. I.

Rudykh, G.A., Semenov, Eh.I. (2000)

Siberian Mathematical Journal

Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II.

Rudykh, G.A., Semenev, Eh.I. (2001)

Siberian Mathematical Journal

Existence and continuity of global attractors for a degenerate semilinear parabolic equation.

Cung The Anh, Tran Dinh Ke (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and nonexistence of global solutions of degenerate and singular parabolic systems.

Caristi, Gabriella (2001)

Abstract and Applied Analysis

Existence and nonexistence results for a class of linear and semilinear parabolic equations related to some Caffarelli-Kohn-Nirenberg inequalities

Boumediene Abdellaoui, Eduardo Colorado, Ireneo Peral (2004)

Journal of the European Mathematical Society

In this work we study the problem $u_{t} {- div (| x |}^{- 2 γ} \nabla u) = λ \frac{u^{α}}{{| x |}^{2 (γ + 1)}} + f$ in $Ω \times (0, T)$ , $u \geq 0$ in $Ω \times (0, T)$ , $u = 0$ on $\partial Ω \times (0, T)$ , $u (x, 0) = u_{0} (x)$ in $Ω$ , $Ω \subset ℝ^{N}$ $(N \geq 2)$ is a bounded regular domain such that $0 \in Ω$ , $λ > 0$ , $α > 0$ , $- \infty < γ < (N - 2) / 2$ , $f$ and $u_{0}$ are positive functions such...

Existence and properties of the Green function for a class of degenerate parabolic equations.

José C. Fernandes, Bruno Franchi (1996)

Revista Matemática Iberoamericana

It is known that degenerate parabolic equations exhibit somehow different phenomena when we compare them with their elliptic counterparts. Thus, the problem of existence and properties of the Green function for degenerate parabolic boundary value problems is not completely solved, even after the contributions of [GN] and [GW4], in the sense that the existence problem is still open, even if the a priori estimates proved in [GN] will be crucial in our approach (...).

Existence and regularity of a global attractor for doubly nonlinear parabolic equations.

El Hachimi, Abderrahmane, El Ouardi, Hamid (2002)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and regularity results for the gradient flow for $p$ -harmonic maps.

Misawa, Masashi (1998)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence and uniqueness of periodic solutions for a model of contaminant flow in porous medium.

Badii, Maurizio (2003)

Rendiconti del Seminario Matematico

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...

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