Search results for "Elliptic boundary value problem"
showing 10 items of 18 documents
Parallel fictitious domain method for a non‐linear elliptic neumann boundary value problem
1999
Parallelization of the algebraic fictitious domain method is considered for solving Neumann boundary value problems with variable coefficients. The resulting method is applied to the parallel solution of the subsonic full potential flow problem which is linearized by the Newton method. Good scalability of the method is demonstrated on a Cray T3E distributed memory parallel computer using MPI in communication. Copyright © 1999 John Wiley & Sons, Ltd.
On Some Properties of the Dirichlet Problem at Resonance
2008
Abstract The boundary value problem at resonance 𝑥″ + 𝑥 = 𝑞 sin 𝑡 + 𝑓(𝑡,𝑥,𝑥′), 𝑥(0) = 0, 𝑥(π) = 0, is considered, where 𝑓 : [0,π] × 𝑹2 → 𝑹 is a bounded Carathéodory function, 𝑞 is a parameter. We state the multiplicity results without assuming that 𝑓 has limits.
Multiple solutions for a discrete boundary value problem involving the p-Laplacian.
2008
Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.
A Parametric Dirichlet Problem for Systems of Quasilinear Elliptic Equations With Gradient Dependence
2016
The aim of this article is to study the Dirichlet boundary value problem for systems of equations involving the (pi, qi) -Laplacian operators and parameters μi≥0 (i = 1,2) in the principal part. Another main point is that the nonlinearities in the reaction terms are allowed to depend on both the solution and its gradient. We prove results ensuring existence, uniqueness, and asymptotic behavior with respect to the parameters.
Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian
2017
Abstract In the framework of variational methods, we use a two non-zero critical points theorem to obtain the existence of two positive solutions to Dirichlet boundary value problems for difference equations involving the discrete p -Laplacian operator.
On Boundary Value Problems for ϕ-Laplacian on the Semi-Infinite Interval
2017
The Dirichlet problem and the problem with functional boundary condition for ϕ-Laplacian on the semi-infinite interval are studied as well as solutions between the lower and upper functions.
Some qualitative properties for the total variation flow
2002
We prove the existence of a finite extinction time for the solutions of the Dirichlet problem for the total variation flow. For the Neumann problem, we prove that the solutions reach the average of its initial datum in finite time. The asymptotic profile of the solutions of the Dirichlet problem is also studied. It is shown that the profiles are nonzero solutions of an eigenvalue-type problem that seems to be unexplored in the previous literature. The propagation of the support is analyzed in the radial case showing a behaviour entirely different to the case of the problem associated with the p-Laplacian operator. Finally, the study of the radially symmetric case allows us to point out othe…
Generalized dirichlet problem in nonlinear potential theory
1990
The operator extending the classical solution of the Dirichlet problem for the quasilinear elliptic equation divA(x,▽u)=0 akin to thep-Laplace equation is shown to be unique providedA obeys a specific order principle. The Keldych lemma is also generalized to this nonlinear setting.
Evolution Problems Associated to Linear Growth Functionals: The Dirichlet Problem
2003
Let Ω be a bounded set inIR N with Lipschitz continuous boundary ∂Ω. We are interested in the problem
Guaranteed error bounds for a class of Picard-Lindelöf iteration methods
2013
We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed