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 A Lyapunov-Type Inequality for a Fractional Differential Equation under a Robin Boundary Condition

2015 ◽  
Vol 2015 ◽  
pp. 1-5 ◽  
Author(s):  
Mohamed Jleli ◽  
Lakhdar Ragoub ◽  
Bessem Samet
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Fractional Differential Equations ◽  
Type Inequality ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Real Zeros ◽  
Fractional Differential ◽  
Robin Boundary ◽  
Lyapunov Type Inequality

We establish a new Lyapunov-type inequality for a class of fractional differential equations under Robin boundary conditions. The obtained inequality is used to obtain an interval where a linear combination of certain Mittag-Leffler functions has no real zeros.

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.

Multiple solutions for an elliptic system with indefinite Robin boundary conditions

2017 ◽  
Vol 8 (1) ◽  
pp. 603-614 ◽  
Author(s):  
Pablo Amster
Keyword(s):  
Boundary Condition ◽  
Elliptic System ◽  
Multiple Solutions ◽  
Robin Boundary Condition ◽  
Robin Boundary Conditions ◽  
Precise Calculation ◽  
Scalar Operator ◽  
Point Operator ◽  
Robin Boundary ◽  
Linear Scalar

Abstract Multiplicity of solutions is proved for an elliptic system with an indefinite Robin boundary condition under an assumption that links the linearisation at 0 and the eigenvalues of the associated linear scalar operator. Our result is based on a precise calculation of the topological degree of a suitable fixed point operator over large and small balls.

scholarly journals Analytical Solutions of One-Dimensional Contaminant Transport in Soils with Source Production-Decay

Soil Systems ◽  
2018 ◽  
Vol 2 (3) ◽  
pp. 40
Author(s):  
Arianna Moranda ◽  
Roberto Cianci ◽  
Ombretta Paladino
Keyword(s):  
Boundary Condition ◽  
Analytical Solutions ◽  
Contaminated Soils ◽  
Radioactive Decay ◽  
Robin Boundary Condition ◽  
One Dimensional ◽  
Advection Dispersion ◽  
Realistic Description ◽  
Liquid Pools ◽  
Robin Boundary

An analytical solution in closed form of the advection-dispersion equation in one-dimensional contaminated soils is proposed in this paper. This is valid for non-conservative solutes with first order reaction, linear equilibrium sorption, and a time-dependent Robin boundary condition. The Robin boundary condition is expressed as a combined production-decay function representing a realistic description of the source release phenomena in time. The proposed model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines, Non Aqueous Phase Liquid pools, or radioactive decay series. The developed analytical model tends towards the known analytical solutions for particular values of the rate constants.

scholarly journals Numerical solution to the Complex 2D Helmholtz Equation based on Finite Volume Method with Impedance Boundary Conditions

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 436-443 ◽  
Author(s):  
Angela Handlovičová ◽  
Izabela Riečanová
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Robin Boundary Condition ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Volume Method ◽  
Robin Boundary

AbstractIn this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.

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.

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