scholarly journals EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR DAMPED LINEAR HYPERBOLIC EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS

2014 ◽  
Vol 95 (2) ◽  
Author(s):  
H. Bennour ◽  
M.S. Said
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Hyperbolic Equations ◽  
Dirichlet Boundary Conditions ◽  
Uniqueness Of Solutions ◽  
Linear Hyperbolic Equations

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.

ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS TO 2D G-BÉNARD PROBLEM IN UNBOUNDED DOMAINS

2020 ◽  
Vol 65 (6) ◽  
pp. 23-30
Author(s):  
Thinh Tran Quang ◽  
Thuy Le Thi
Keyword(s):  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Stokes Equations ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Bénard Problem ◽  
Benard Problem ◽  
Homogeneous Dirichlet Boundary Conditions

We consider the 2D g-Bénard problem in domains satisfying the Poincaré inequality with homogeneous Dirichlet boundary conditions. We prove the existence and uniqueness of global weak solutions. The obtained results particularly extend previous results for 2D g-Navier-Stokes equations and 2D Bénard problem.

Global attractor for a hyperbolic Cahn–Hilliard equation with a proliferation term

2021 ◽  
pp. 1-23
Author(s):  
Padouette Boubati Badieti Matala ◽  
Daniel Moukoko ◽  
Mayeul Evrard Isseret Goyaud
Keyword(s):  
Boundary Conditions ◽  
Hyperbolic Equation ◽  
Global Attractor ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Hilliard Equation ◽  
Uniqueness Of The Solution ◽  
Cahn Hilliard Equation

In this article, we study a hyperbolic equation of Cahn–Hilliard with a proliferation term and Dirichlet boundary conditions. In particular, we prove the existence and uniqueness of the solution, and also the existence of the global attractor.

The semilinear heat equation with a Heaviside source term

1992 ◽  
Vol 3 (4) ◽  
pp. 367-379 ◽  
Author(s):  
Roberto Gianni ◽  
Josephus Hulshof
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Initial Value Problem ◽  
Source Term ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Bounded Interval ◽  
Semilinear Heat Equation

We consider the initial value problem for the equation ut = uxx + H(u), where H is the Heaviside graph, on a bounded interval with Dirichlet boundary conditions, and discuss existence, regularity and uniqueness of solutions and interfaces.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Charge algebra in Al(A)dSn spacetimes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Adrien Fiorucci ◽  
Romain Ruzziconi
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Three Dimensional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Structure ◽  
Asymptotic Symmetry ◽  
Renormalization Procedure ◽  
Field Dependent ◽  
Odd Dimensions

Abstract The gravitational charge algebra of generic asymptotically locally (A)dS spacetimes is derived in n dimensions. The analysis is performed in the Starobinsky/Fefferman-Graham gauge, without assuming any further boundary condition than the minimal falloffs for conformal compactification. In particular, the boundary structure is allowed to fluctuate and plays the role of source yielding some symplectic flux at the boundary. Using the holographic renormalization procedure, the divergences are removed from the symplectic structure, which leads to finite expressions. The charges associated with boundary diffeomorphisms are generically non-vanishing, non-integrable and not conserved, while those associated with boundary Weyl rescalings are non-vanishing only in odd dimensions due to the presence of Weyl anomalies in the dual theory. The charge algebra exhibits a field-dependent 2-cocycle in odd dimensions. When the general framework is restricted to three-dimensional asymptotically AdS spacetimes with Dirichlet boundary conditions, the 2-cocycle reduces to the Brown-Henneaux central extension. The analysis is also specified to leaky boundary conditions in asymptotically locally (A)dS spacetimes that lead to the Λ-BMS asymptotic symmetry group. In the flat limit, the latter contracts into the BMS group in n dimensions.

scholarly journals Fibonacci wavelet method for solving time-fractional telegraph equations with Dirichlet boundary conditions

2021 ◽  
pp. 104123
Author(s):  
Firdous A. Shah ◽  
Mohd Irfan ◽  
Kottakkaran S. Nisar ◽  
R.T. Matoog ◽  
Emad E. Mahmoud
Keyword(s):  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Wavelet Method ◽  
Telegraph Equations
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