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Let $f$ be an odd function of a class $C^{2}$ such that $f (1) = 0, f^{'} (0) < 0, f^{'} (1) > 0$ and $x \mapsto f (x) / x$ increases on $[0, 1]$ . We approximate the positive solution of $- Δ u + f (u) = 0,$ on $ℝ_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $- Δ u_{L} + f (u_{L}) = 0,$ on ${] 0, L [}^{2}$ with adequate non-homogeneous Dirichlet conditions. We show that the error $u_{L} - u$ tends to zero exponentially fast, in the uniform norm.

Approximation of a semilinear elliptic problem in an unbounded domain

Messaoud Kolli, Michelle Schatzman (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Let f be an odd function of a class C2 such that ƒ(1) = 0,ƒ'(0) < 0,ƒ'(1) > 0 and $x \mapsto f (x) / x$ increases on [0,1]. We approximate the positive solution of Δu + ƒ(u) = 0, on $_{+}^{2}$ with homogeneous Dirichlet boundary conditions by the solution of $- Δ u_{L} + f (u_{L}) = 0,$ on ]0,L[2 with adequate non-homogeneous Dirichlet conditions. We show that the error uL - u tends to zero exponentially fast, in the uniform norm.

Approximation of solution branches for semilinear bifurcation problems

Laurence Cherfils (1999)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Approximation of solution branches for semilinear bifurcation problems

Laurence Cherfils (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This note deals with the approximation, by a P1 finite element method with numerical integration, of solution curves of a semilinear problem. Because of both mixed boundary conditions and geometrical properties of the domain, some of the solutions do not belong to H2. So, classical results for convergence lead to poor estimates. We show how to improve such estimates with the use of weighted Sobolev spaces together with a mesh “a priori adapted” to the singularity. For the H1 or L2-norms, we...

Approximation of the Heaviside function and uniqueness results for a class of quasilinear elliptic-parabolic problems.

G. Gagneux, F. Guerfi (1990)

Revista Matemática de la Universidad Complutense de Madrid

In this paper, we concern ourselves with uniqueness results for an elliptic-parabolic quasilinear partial differential equation describing, for instance, the pressure of a fluid in a three-dimensional porous medium: within the frame of mathematical modeling of the secondary recovery from oil fields, the handling of the component conservation laws leads to a system including such a pressure equation, locally elliptic or parabolic according to the evolution of the gas phase.

A-Priori Schranken für Lösungen gewisser elliptischer Probleme.

Michael Wiegner (1976)

Manuscripta mathematica

Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

Olivier Rey, Juncheng Wei (2005)

Journal of the European Mathematical Society

We show that the critical nonlinear elliptic Neumann problem $Δ u - μ u + u^{7 / 3} = 0$ in $Ω$ , $u > 0$ in $Ω$ , $\frac{\partial u}{\partial ν} = 0$ on $\partial Ω$ , where $Ω$ is a bounded and smooth domain in $ℝ^{5}$ , has arbitrarily many solutions, provided that $μ > 0$ is small enough. More precisely, for any positive integer $K$ , there exists $μ_{K} > 0$ such that for $0 < μ < μ_{K}$ , the above problem has a nontrivial solution which blows up at $K$ interior points in $Ω$ , as $μ \to 0$ . The location of the blow-up points is related to the domain geometry. The solutions are obtained as critical points of some finite-dimensional...

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An ODE approach to the equation ... U + Ku ... = 0, in Rn.

An optimization problem in heat conduction

An Orlicz-Sobolev space setting for quasilinear elliptic problems.

An upper bound for positive solutions of the equation $Δ u = u^{α}$ .

Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation

Analytic aspects of quasiconformality.

Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres.

Annulus oscillation criteria for second order nonlinear elliptic differential equations with damping.

Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations.

Applicazioni della teoria dello scattering all’operatore di Laplace-Beltrami sulle forme differenziali

Approximation of a semilinear elliptic problem in an unbounded domain

Approximation of a semilinear elliptic problem in an unbounded domain

Approximation of solution branches for semilinear bifurcation problems

Approximation of solution branches for semilinear bifurcation problems

Approximation of the Heaviside function and uniqueness results for a class of quasilinear elliptic-parabolic problems.

A-Priori Schranken für Lösungen gewisser elliptischer Probleme.

Arbitrary number of positive solutions for an elliptic problem with critical nonlinearity

Associated families of pluriharmonic maps and isotropy.

Asymmetric elliptic problems in $ℝ^{N}$ .

Asymmetric elliptic problems with indefinite weights

Currently displaying 141 – 160 of 180