On a class of forward–backward parabolic equations: Existence of solutions

2018 ◽  
Vol 177 ◽  
pp. 46-87 ◽  
Author(s):  
Michiel Bertsch ◽  
Flavia Smarrazzo ◽  
Alberto Tesei
Keyword(s):  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Backward Parabolic Equations

Conditional stability for backward parabolic equations with LogLipt×Lipx-coefficients

2015 ◽  
Vol 121 ◽  
pp. 101-122 ◽  
Author(s):  
Daniele Del Santo ◽  
Christian P. Jäh ◽  
Martino Prizzi
Keyword(s):  
Parabolic Equations ◽  
Conditional Stability ◽  
Backward 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.

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