Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection.
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence de la trace initiale pour des solutions d'une équation parabolique dégénérée
Existence for a Cauchy-Dirichlet problem for evolutional p-Laplacian systems
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
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 for -Laplacian parabolic equation in .
Existence of solutions for a degenerate nonlinear evolution equation.
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.
Existence of weak solutions to doubly degenerate diffusion equations
We prove existence of weak solutions to doubly degenerate diffusion equations by Faedo-Galerkin approximation for general domains and general nonlinearities. More precisely, we discuss the equation in an abstract setting, which allows to choose function spaces corresponding to bounded or unbounded domains with Dirichlet or Neumann boundary conditions. The function can be an inhomogeneity or a nonlinearity involving terms of the form or . In the appendix, an introduction to weak differentiability...
Existence result for variational degenerated parabolic problems via pseudo-monotonicity.
Existence Results for Doubly Nonlinear Higher Order Parabolic Equations on Unbounded Domains.
Existence results for some nonlinear parabolic equations with degenerate coercivity and singular lower-order terms
In this paper, we study the existence results for some parabolic equations with degenerate coercivity, singular lower order term depending on the gradient, and positive initial data in .
Explicit parametrix and local limit theorems for some degenerate diffusion processes
For a class of degenerate diffusion processes of rank 2, i.e. when only Poisson brackets of order one are needed to span the whole space, we obtain a parametrix representation of McKean–Singer [J. Differential Geom.1 (1967) 43–69] type for the density. We therefrom derive an explicit gaussian upper bound and a partial lower bound that characterize the additional singularity induced by the degeneracy. This particular representation then allows to give a local limit theorem with the usual convergence...
Extinction and decay estimates of solutions for a class of porous medium equations.
Extinction for fast diffusion equations with nonlinear sources.