Existence and uniqueness of entropy solutions to nonlinear parabolic problem with homogeneous Dirichlet boundary conditions involving variable exponent

SeMA Journal ◽  
2018 ◽  
Vol 76 (1) ◽  
pp. 153-180
Author(s):  
Bila Adolphe Kyelem ◽  
Arouna Ouedraogo ◽  
Frédéric D. Y. Zongo
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Parabolic Problem ◽  
Variable Exponent ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Entropy Solutions ◽  
Nonlinear Parabolic Problem ◽  
Nonlinear Parabolic ◽  
Homogeneous Dirichlet Boundary Conditions

A Lane–Emden system with singular data

2011 ◽  
Vol 141 (6) ◽  
pp. 1279-1294 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Boundary Conditions ◽  
Elliptic System ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Singular Data

We study the elliptic system −Δu = δ(x)−avp in Ω, −Δv = δ(x)−buq in Ω, subject to homogeneous Dirichlet boundary conditions. Here, Ω ⊂ ℝN, N ≥ 1, is a smooth and bounded domain, δ(x) = dist(x, ∂Ω), a, b ≥ 0 and p, q ∈ ℝ satisfy pq > −1. The existence, non-existence and uniqueness of solutions are investigated in terms of a, b, p and q.

scholarly journals A biharmonic equation with singular nonlinearity

2011 ◽  
Vol 55 (1) ◽  
pp. 155-166 ◽  
Author(s):  
Marius Ghergu
Keyword(s):  
Green Function ◽  
Boundary Conditions ◽  
Bounded Domain ◽  
Existence And Uniqueness ◽  
Biharmonic Equation ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Biharmonic Operator ◽  
The Green Function ◽  
Uniqueness Of A Solution

AbstractWe study the biharmonic equation Δ2u=u−α, 0 < α < 1, in a smooth and bounded domain Ω ⊂ ℝn,n≥ 2, subject to Dirichlet boundary conditions. Under some suitable assumptions on Ω related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.

Nonlinear Dirichlet problem with non local regional diffusion

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
César E. Torres Ledesma
Keyword(s):  
Dirichlet Problem ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions ◽  
Nonlinear Dirichlet Problem ◽  
Non Local ◽  
Homogeneous Dirichlet Boundary Conditions

AbstractThe purpose of this paper is to study the existence of solutions for equations driven by a non-local regional operator with homogeneous Dirichlet boundary conditions. More precisely, we consider the problemwhere the nonlinear term

LEAST ENERGY NODAL SOLUTIONS OF THE BREZIS–NIRENBERG PROBLEM IN DIMENSION N = 5

2009 ◽  
Vol 11 (01) ◽  
pp. 59-69 ◽  
Author(s):  
PAOLO ROSELLI ◽  
MICHEL WILLEM
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
First Eigenvalue ◽  
Nodal Solutions ◽  
The First Eigenvalue ◽  
Homogeneous Dirichlet Boundary Conditions ◽  
Sign Changing Solutions ◽  
Nirenberg Problem ◽  
Least Energy

We prove the existence of (a pair of) least energy sign changing solutions of [Formula: see text] when Ω is a bounded domain in ℝN, N = 5 and λ is slightly smaller than λ1, the first eigenvalue of -Δ with homogeneous Dirichlet boundary conditions on Ω.

scholarly journals Existence and uniqueness of solution for Cahn-Hilliard hyperbolic phase field system with Dirichlet boundary conditions and polynomial potential

2018 ◽  
Vol 7 (1) ◽  
pp. 10
Author(s):  
A. J. Bissouesse ◽  
Daniel Moukoko ◽  
Franck Langa ◽  
Macaire Batchi
Keyword(s):  
Boundary Conditions ◽  
Phase Field ◽  
Dirichlet Boundary ◽  
Initial Conditions ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solution ◽  
Polynomial Potential ◽  
Field System ◽  
Phase Field System ◽  
Homogeneous Dirichlet Boundary Conditions

Our aim in this article is to study the existence and the uniqueness of solution for Cahn-Hilliard hyperbolic phase-field system, with initial conditions, homogeneous Dirichlet boundary conditions, polynomial potential in a bounded and smooth domain.

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