Renormalized solutions of elliptic equations with Robin boundary conditions

2017 ◽  
Vol 37 (4) ◽  
pp. 889-910
Author(s):  
Olivier GUIBÉ ◽  
Alip OROPEZA
Keyword(s):  
Boundary Conditions ◽  
Elliptic Equations ◽  
Robin Boundary Conditions ◽  
Renormalized Solutions ◽  
Robin Boundary

scholarly journals Maximum principles for a class of semilinear elliptic boundary-value problems

1995 ◽  
Vol 52 (1) ◽  
pp. 169-175 ◽  
Author(s):  
Zhang Hailiang
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Elliptic Boundary ◽  
Maximum Principles ◽  
Robin Boundary Conditions ◽  
Elliptic Boundary Value ◽  
Physical Problems ◽  
Semilinear Elliptic ◽  
Robin Boundary

For years it has remained a problem to find suitable functionals satisfying certain maximum principles for solutions of the equation Δu + f(x, u) = 0. In this paper, maximum principles for certain functionals which are defined on solutions of semilinear elliptic equations subject to mixed or Robin boundary conditions are obtained. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.

scholarly journals An efficient adaptive grid method for a system of singularly perturbed convection-diffusion problems with Robin boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Li-Bin Liu ◽  
Ying Liang ◽  
Xiaobing Bao ◽  
Honglin Fang
Keyword(s):  
Boundary Conditions ◽  
Grid Method ◽  
Posteriori Error ◽  
Adaptive Grid ◽  
Singularly Perturbed ◽  
Robin Boundary Conditions ◽  
Euler Formula ◽  
Convection Diffusion ◽  
Backward Euler ◽  
Robin Boundary

AbstractA system of singularly perturbed convection-diffusion equations with Robin boundary conditions is considered on the interval $[0,1]$ [ 0 , 1 ] . It is shown that any solution of such a problem can be expressed to a system of first-order singularly perturbed initial value problem, which is discretized by the backward Euler formula on an arbitrary nonuniform mesh. An a posteriori error estimation in maximum norm is derived to design an adaptive grid generation algorithm. Besides, in order to establish the initial values of the original problems, we construct a nonlinear optimization problem, which is solved by the Nelder–Mead simplex method. Numerical results are given to demonstrate the performance of the presented method.

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