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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...

Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection.

Fang, Zhong Bo, Piao, Daxiong, Wang, Jian (2009)

Boundary Value Problems [electronic only]

Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée

Abdelilah Gmira (1986/1987)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée

Abdelilah Gmira (1988)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems

Masashi Misawa (2004)

Applicationes Mathematicae

We study the existence of a weak solution to a Cauchy-Dirichlet problem for evolutional p-Laplacian systems with constant coefficients and principal term only. The initial-boundary data is assumed to be a bounded weak solution of an evolutional p-Laplacian system with an L¹-function as external force. The key ingredient is the maximum principle for weak solutions.

Existence of blow-up solutions for a degenerate parabolic-elliptic Keller–Segel system with logistic source

Yuya Tanaka (2023)

Archivum Mathematicum

This paper deals with existence of finite-time blow-up solutions to a degenerate parabolic–elliptic Keller–Segel system with logistic source. Recently, finite-time blow-up was established for a degenerate Jäger–Luckhaus system with logistic source. However, blow-up solutions of the aforementioned system have not been obtained. The purpose of this paper is to construct blow-up solutions of a degenerate Keller–Segel system with logistic source.

Existence of global attractors in $L^{p}$ for $m$ -Laplacian parabolic equation in $ℝ^{N}$ .

Chen, Caisheng, Shi, Lanfang, Wang, Hui (2009)

Boundary Value Problems [electronic only]

Existence of solutions for a degenerate nonlinear evolution equation.

A. Sanih Bonfoh (2005)

RACSAM

We consider a model of generalized Cahn-Hilliard equations with a logarithmic free energy and a degenerate mobility, and obtain a result on the existence of solutions.

Existence of solutions for a degenerate seawater intrusion problem.

El Alaoui Talibi, Mohamed, Tber, Moulay Hicham (2005)

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

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