A computational method for solving one-dimensional variable-coefficient Burgers equation

2007 ◽  
Vol 188 (2) ◽  
pp. 1389-1401 ◽  
Author(s):  
Minggen Cui ◽  
Fazhan Geng
Keyword(s):  
Variable Coefficient ◽  
Burgers Equation ◽  
Computational Method ◽  
One Dimensional ◽  
Dimensional Variable

Explicit Analytical Solutions of Linear and Nonlinear Interior Heat and Mass Transfer Equation Sets for Drying Process

2003 ◽  
Vol 125 (1) ◽  
pp. 175-178 ◽  
Author(s):  
Ruixian Cai ◽  
Na Zhang
Keyword(s):  
Analytical Solutions ◽  
Variable Coefficient ◽  
Infinite Plate ◽  
Explicit Solutions ◽  
Drying Process ◽  
Mass Transfer Equation ◽  
Mathematical Skills ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Dimensional Variable

Some algebraic explicit analytical solutions of the unsteady one-dimensional variable coefficient partial differential equation set describing drying process of an infinite plate are derived and given. Such explicit solutions have not yet been published before. Besides their irreplaceable theoretical value, analytical solutions can also serve as benchmark to check the results of recently rapidly developing numerical calculation and study various computational methods. In addition, some mathematical skills used in this paper are special and deserve further attention.

scholarly journals On a stochastic Burgers equation with Dirichlet boundary conditions

2003 ◽  
Vol 2003 (43) ◽  
pp. 2735-2746 ◽  
Author(s):  
Ekaterina T. Kolkovska
Keyword(s):  
Weak Solution ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Burgers Equation ◽  
Martingale Problem ◽  
Weak Limit ◽  
Dirichlet Boundary Conditions ◽  
One Dimensional ◽  
Stochastic Burgers Equation ◽  
The One

We consider the one-dimensional Burgers equation perturbed by a white noise term with Dirichlet boundary conditions and a non-Lipschitz coefficient. We obtain existence of a weak solution proving tightness for a sequence of polygonal approximations for the equation and solving a martingale problem for the weak limit.

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