Existence theorems for some elliptic systems.
Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in
For a bounded domain , we use the notion of very weak solutions to obtain a new and large uniqueness class for solutions of the inhomogeneous Navier-Stokes system , , with , , and very general data classes for , , such that may have no differentiability property. For smooth data we get a large class of unique and regular solutions extending well known classical solution classes, and generalizing regularity results. Moreover, our results are closely related to those of a series of...
Existencia De Multiples Soluciones De Un Problema Eliptico Con Parte Lineal En Resonancia Con El Primer Valor Propio.
Exit time, Green function and semilinear elliptic equations.
Expanded mixed finite element methods for quasilinear second order elliptic problems, II
Explicit construction, uniqueness, and bifurcation curves of solutions for a nonlinear Dirichlet problem in a ball.
Extension of Díaz-Saá's inequality in RN and application to a system of p-Laplacian.
The purpose of this paper is to extend the Díaz-Saá’s inequality for the unbounded domains as RN.The proof is based on the Picone’s identity which is very useful in problems involving p-Laplacian. In a second part, we study some properties of the first eigenvalue for a system of p-Laplacian. We use Díaz-Saá’s inequality to prove uniqueness and Egorov’s theorem for the isolation. These results generalize J. Fleckinger, R. F. Manásevich, N. M. Stavrakakis and F. de Thélin’s work [9] for the first...
Extremal equilibria for parabolic non-linear reaction-diffusion equations
Extremal solutions for nonlinear neumann problems
In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.
Finite Dimensional Approximation of Nonlinear Problems. Part II : Limit Points.
Finite Dimensional Approximation of Nonlinear Problems. Part III : Simple Bifurcation Points.
Finite element approximation of a model reaction - diffusion problem with a non-Lipschitz nonlinearity.
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite element approximation of nonlinear elliptic problems with discontinuous coefficients
Finite Element Error Estimates for Non-Linear Elliptic Equations of Monotone Type.
Finite Element Solution of Nonlinear Elliptic Problems.
Finite element solutions for radiation cooling problems with nonlinear boundary conditions
Finite volume schemes for fully non-linear elliptic equations in divergence form
We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the -laplacian kind: (with ). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.
Finite volume schemes for fully non-linear elliptic equations in divergence form
We construct finite volume schemes, on unstructured and irregular grids and in any space dimension, for non-linear elliptic equations of the p-Laplacian kind: -div(|∇u|p-2∇u) = ƒ (with 1 < p < ∞). We prove the existence and uniqueness of the approximate solutions, as well as their strong convergence towards the solution of the PDE. The outcome of some numerical tests are also provided.
Finite volume schemes for the p-laplacian on cartesian meshes
This paper is concerned with the finite volume approximation of the p-laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes. A reconstruction of the norm of the gradient on the mesh’s interfaces is needed in order to discretize the p-laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...