Global existence of solutions to one-phase Stefan problems for semilinear parabolic equations

1998 ◽  
Vol 175 (1) ◽  
pp. 327-337 ◽  
Author(s):  
Toyohiko Aiki ◽  
Hitoshi Imai
Keyword(s):  
Global Existence ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Semilinear Parabolic Equations ◽  
Stefan Problems ◽  
Global Existence Of Solutions ◽  
Semilinear Parabolic

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.

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