Correctness of the first boundary-value problem and the Cauchy problem for some quasilinear parabolic systems without conditions at infinity

2006 ◽  
Vol 135 (1) ◽  
pp. 2625-2636 ◽  
Author(s):  
N. M. Bokalo
Keyword(s):  
Cauchy Problem ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Parabolic Systems ◽  
Quasilinear Parabolic Systems ◽  
The Cauchy Problem ◽  
Conditions At Infinity ◽  
Quasilinear Parabolic

A finite difference method for the very weak solution to a Cauchy problem for an elliptic equation

2018 ◽  
Vol 26 (6) ◽  
pp. 835-857 ◽  
Author(s):  
Dinh Nho Hào ◽  
Le Thi Thu Giang ◽  
Sergey Kabanikhin ◽  
Maxim Shishlenin
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Finite Difference ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Weak Sense ◽  
Very Weak Solution ◽  
Local Boundary ◽  
The Cauchy Problem ◽  
Non Local

Abstract We introduce the concept of very weak solution to a Cauchy problem for elliptic equations. The Cauchy problem is regularized by a well-posed non-local boundary value problem whose solution is also understood in a very weak sense. A stable finite difference scheme is suggested for solving the non-local boundary value problem and then applied to stabilizing the Cauchy problem. Some numerical examples are presented for showing the efficiency of the method.

Sign in / Sign up

Export Citation Format

Share Document