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 Erratum to: Uniqueness of renormalized solutions for a class of parabolic equations

2017 ◽  
Vol 66 (2) ◽  
pp. 645-645
Author(s):  
Ahmed Aberqi ◽  
Jaouad Bennouna ◽  
Mohamed Hammoumi
Keyword(s):  
Parabolic Equations ◽  
Renormalized Solutions

scholarly journals Uniqueness of renormalized solutions to nonlinear parabolic problems with lower-order terms

2013 ◽  
Vol 143 (6) ◽  
pp. 1185-1208 ◽  
Author(s):  
Rosaria Di Nardo ◽  
Filomena Feo ◽  
Olivier Guibé
Keyword(s):  
Parabolic Equations ◽  
Dirichlet Boundary ◽  
Growth Conditions ◽  
Dirichlet Boundary Conditions ◽  
Parabolic Problems ◽  
Renormalized Solutions ◽  
Uniqueness Results ◽  
Nonlinear Parabolic ◽  
Image Position ◽  
Lower Order Terms

We consider a general class of parabolic equations of the typewith Dirichlet boundary conditions and with a right-hand side belonging to L1 + Lp′ (W−1, p′). Using the framework of renormalized solutions we prove uniqueness results under appropriate growth conditions and Lipschitz-type conditions on a(u, ∇u), K(u) and H(∇u).

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