Existence of solutions for a nonlinear system of parabolic equations with gradient flow structure

2013 ◽  
Vol 174 (4) ◽  
pp. 653-679 ◽  
Author(s):  
Jonathan Zinsl
Keyword(s):  
Nonlinear System ◽  
Flow Structure ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Gradient Flow ◽  
System Of Parabolic Equations

scholarly journals Parabolic inequalities inL1as limits of renormalized equations

2006 ◽  
Vol 2006 ◽  
pp. 1-18
Author(s):  
K. Azelmat ◽  
M. Kbiri Alaoui ◽  
D. Meskine ◽  
A. Souissi
Keyword(s):  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Renormalized Solutions ◽  
Parabolic Inequalities

The paper deals with the existence of solutions of some parabolic bilateral problems approximated by the renormalized solutions of some parabolic equations.

scholarly journals Multidimensional computational models of gas combustion in heterogeneous porous medium

2021 ◽  
Vol 2099 (1) ◽  
pp. 012010
Author(s):  
Yu Laevsky ◽  
T Nosova
Keyword(s):  
Porous Medium ◽  
Parabolic Equations ◽  
Computational Models ◽  
Front Propagation ◽  
Original Model ◽  
Gas Mixture ◽  
Heterogeneous Porous Medium ◽  
Gas Combustion ◽  
Piecewise Constant ◽  
System Of Parabolic Equations

Abstract The processes of filtration gas combustion in heterogeneous porous medium is studying. The presence of two opposite modes of front propagation made it possible to stabilize the combustion front in a composite porous medium with piecewise constant porosity. A feature of this study is the presentation of the original model not in the traditional form of a system of parabolic equations, but in the form of integral conservation laws in terms of the temperature of the porous medium, the total gas enthalpy, and the mass of gas mixture, and the fluxes corresponding to these functions.

Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term

2013 ◽  
Vol 143 (3) ◽  
pp. 643-668 ◽  
Author(s):  
Haifeng Shang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Global Solvability ◽  
Gradient Term ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Limiting Case

We study the Cauchy problem for the degenerate and uniformly parabolic equations with gradient term. The local existence, global existence and non-existence of solutions are obtained. In the case of global solvability, we get the exact estimates of a solution. In particular, we obtain the global existence of solutions in the limiting case.

GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF A TUMOR ANGIOGENESIS MODEL WITH CHEMOTAXIS AND HAPTOTAXIS

2013 ◽  
Vol 24 (03) ◽  
pp. 427-464 ◽  
Author(s):  
CRISTIAN MORALES-RODRIGO ◽  
J. IGNACIO TELLO
Keyword(s):  
Global Existence ◽  
Tumor Angiogenesis ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Asymptotically Stable ◽  
System Of Differential Equations ◽  
Homogeneous Steady State ◽  
Global Existence Of Solutions ◽  
Extra Assumption ◽  
Angiogenesis Model

We consider a system of differential equations modeling tumor angiogenesis. The system consists of three equations: two parabolic equations with chemotactic terms to model endothelial cells and tumor angiogenesis factors coupled to an ordinary differential equation which describes the evolution of the fibronectin concentration. We study global existence of solutions and, under extra assumption on the initial data of the fibronectin concentration we obtain that the homogeneous steady state is asymptotically stable.

Sign in / Sign up

Export Citation Format

Share Document