scholarly journals Global solutions to cross diffusion parabolic systems on 2D domains

2015 ◽  
Vol 143 (7) ◽  
pp. 2999-3010 ◽  
Author(s):  
Dung Le ◽  
Vu Thanh Nguyen
Keyword(s):  
Global Solutions ◽  
Parabolic Systems ◽  
Cross Diffusion

scholarly journals Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion

2004 ◽  
Vol 10 (3) ◽  
pp. 719-730 ◽  
Author(s):  
Y. S. Choi ◽  
◽  
Roger Lui ◽  
Yoshio Yamada ◽  
◽  
...  
Keyword(s):  
Global Solutions ◽  
Strongly Coupled ◽  
Cross Diffusion

Convergence of diffusive BGK approximations for nonlinear strongly parabolic systems

2002 ◽  
Vol 132 (2) ◽  
pp. 341-358 ◽  
Author(s):  
Corrado Lattanzio ◽  
Roberto Natalini
Keyword(s):  
Space Dimension ◽  
Global Solutions ◽  
Parabolic Systems ◽  
Compensated Compactness ◽  
Rigorous Result ◽  
Formal Limit ◽  
One Space Dimension

We study a class of BGK approximations of parabolic systems in one space dimension. We prove stability and existence of global solutions for this model. Moreover, under certain conditions, we prove a rigorous result of convergence toward the formal limit, by using compensated compactness techniques.

scholarly journals Mathematical modeling of double nonlinear problem of reaction diffusion in not divergent form with a source and variable density

2021 ◽  
Vol 2131 (3) ◽  
pp. 032043
Author(s):  
M Aripov ◽  
A S Matyakubov ◽  
J O Khasanov ◽  
M M Bobokandov
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equation ◽  
Nonlinear Parabolic Equation ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Variable Density ◽  
Divergence Form ◽  
Cross Diffusion ◽  
Nonlinear Parabolic ◽  
The Cauchy Problem

Abstract In this paper the properties of solutions of nonlinear parabolic equation not in divergence form | x | − 1 ∂ u ∂ t = u q ∂ ∂ x ( | x | n u m − 1 | ∂ u k ∂ x | p − 2 ∂ u ∂ x ) + | x | − 1 u β are studied. Depending on values of the numerical parameters and the initial value, the existence of the global solutions of the Cauchy problem is proved. Constructed asymptotic representation of self-similar solutions of nonlinear parabolic equation not in divergence form, depending on the value in the equation of the numerical parameters necessary and sufficient signs of their existence. The compactly supported solution of the Cauchy problem for a cross-diffusion parabolic equation not in divergence form with a source and a variable density is obtained.

Sign in / Sign up

Export Citation Format

Share Document