scholarly journals An algebraic solution for a 2-D partial differential energy equation with a Robin boundary condition generated from the simpler solution for a Dirichlet boundary condition

1997 ◽  
Vol 34 (10) ◽  
pp. 101-114
Author(s):  
A. Campo ◽  
L. Campo
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Energy Equation ◽  
Dirichlet Boundary ◽  
Robin Boundary Condition ◽  
Algebraic Solution ◽  
Partial Differential ◽  
Robin Boundary

REINFORCEMENT OF THE POISSON EQUATION BY A THIN LAYER

2011 ◽  
Vol 21 (05) ◽  
pp. 1153-1192 ◽  
Author(s):  
JINGYU LI ◽  
KAIJUN ZHANG
Keyword(s):  
Boundary Condition ◽  
Shear Modulus ◽  
Poisson Equation ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Neumann Boundary ◽  
Robin Boundary Condition ◽  
Oscillation Period ◽  
The Poisson Equation ◽  
Robin Boundary

We consider the problem of reinforcing an elastic medium by a strong, rough, thin external layer. This model is governed by the Poisson equation with homogeneous Dirichlet boundary condition. We characterize the asymptotic behavior of the solution as the shear modulus of the layer goes to infinity. We find that there are four types of behaviors: the limiting solution satisfies Poisson equation with Dirichlet boundary condition, Robin boundary condition or Neumann boundary condition, or the limiting solution does not exist. The specific type depends on the integral of the load on the medium, the curvature of the interface and the scaling relations among the shear modulus, the thickness and the oscillation period of the layer.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

A Robin boundary value problem for the Cauchy–Riemann operator in a ring domain

2022 ◽  
Vol 0 (0) ◽  
Author(s):  
İlker Gençtürk ◽  
Yankis R. Linares
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Ring Domain ◽  
Riemann Equation ◽  
Robin Condition ◽  
Cauchy Riemann ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

Abstract In this paper, we study a Robin condition for the inhomogeneous Cauchy–Riemann equation w z ¯ = f {w_{\bar{z}}=f} in a ring domain R, by reformulating it as a Dirichlet boundary condition.

scholarly journals Numerical Solution of Heat Equation with Singular Robin Boundary Condition

2018 ◽  
Vol 19 (2) ◽  
pp. 209
Author(s):  
German Lozada-Cruz ◽  
Cosme Eustaquio Rubio-Mercedes ◽  
Junior Rodrigues-Ribeiro
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Numerical Solution ◽  
Dirichlet Boundary ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Positive Parameter ◽  
One Dimensional ◽  
Small Positive Parameter ◽  
Robin Boundary

In this work we study the numerical solution of one-dimensional heatdiffusion equation with a small positive parameter subject to Robin boundary conditions. The simulations examples lead us to conclude that the numerical solutionsof the differential equation with Robin boundary condition are very close of theanalytic solution of the problem with homogeneous Dirichlet boundary conditionswhen tends to zero

scholarly journals Concentrating solutions for a planar elliptic problem with large nonlinear exponent and Robin boundary condition

2019 ◽  
Vol 8 (1) ◽  
pp. 1252-1285
Author(s):  
Yibin Zhang ◽  
Lei Shi
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Dirichlet Boundary ◽  
Smooth Boundary ◽  
Robin Boundary Condition ◽  
Unit Vector ◽  
Large Exponent ◽  
Concentrating Solutions ◽  
Robin Boundary ◽  
Robin Boundary Value Problem

Abstract Let Ω ⊂ ℝ2 be a bounded domain with smooth boundary and b(x) > 0 a smooth function defined on ∂Ω. We study the following Robin boundary value problem: $$\begin{array}{} \displaystyle \left\{ \begin{alignedat}{2} &{\it\Delta} u+u^p=0 &\quad& \text{in }{\it\Omega},\\ &u>0 &\quad& \text{in }{\it\Omega},\\ &\frac{\partial u}{\partial\nu} +\lambda b(x)u=0 &\quad& \text{on } \partial{\it\Omega}, \end{alignedat} \right. \end{array}$$ where ν denotes the exterior unit vector normal to ∂Ω, 0 < λ < +∞ and p > 1 is a large exponent. We construct solutions of this problem which exhibit concentration as p → +∞ and simultaneously as λ → +∞ at points that get close to the boundary, and show that in general the set of solutions of this problem exhibits a richer structure than the problem with Dirichlet boundary condition.

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

Sign in / Sign up

Export Citation Format

Share Document