Continuous Dependence Results for Parabolic Problems Under Robin Boundary Conditions

2009 ◽  
Vol 30 (1-2) ◽  
pp. 121-135
Author(s):  
M. Marras ◽  
S. Vernier Piro
Keyword(s):  
Boundary Conditions ◽  
Continuous Dependence ◽  
Parabolic Problems ◽  
Robin Boundary Conditions ◽  
Robin Boundary ◽  
Continuous Dependence Results

scholarly journals Blow-Up Solutions and Global Existence for Quasilinear Parabolic Problems with Robin Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Juntang Ding
Keyword(s):  
Boundary Conditions ◽  
Global Solution ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Parabolic Problems ◽  
Robin Boundary Conditions ◽  
Quasilinear Parabolic Problems ◽  
Robin Boundary ◽  
Upper Estimate ◽  
Quasilinear Parabolic

We study the blow-up and global solutions for a class of quasilinear parabolic problems with Robin boundary conditions. By constructing auxiliary functions and using maximum principles, the sufficient conditions for the existence of blow-up solution, an upper bound for the “blow-up time,” an upper estimate of the “blow-up rate,” the sufficient conditions for the existence of global solution, and an upper estimate of the global solution are specified.

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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