scholarly journals Existence of solutions for infinite systems of parabolic equations with functional dependence

2005 ◽  
Vol 86 (2) ◽  
pp. 123-135 ◽  
Author(s):  
Anna Pudełko
Keyword(s):  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Functional Dependence ◽  
Infinite Systems ◽  
Systems Of Parabolic Equations

Stability in 𝐿𝑞-norm for inverse source parabolic problems

2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig
Keyword(s):  
Parabolic Equations ◽  
Main Tool ◽  
Parabolic Systems ◽  
Carleman Estimates ◽  
Parabolic Problems ◽  
Lebesgue Spaces ◽  
First Order ◽  
Lipschitz Estimates ◽  
Systems Of Parabolic Equations

AbstractWe consider systems of parabolic equations coupled in zero and first order terms. We establish Lipschitz estimates in {L^{q}}-norms, {2\leq q\leq\infty}, for the source in terms of the solution in a subdomain. The main tool is a family of appropriate Carleman estimates with general weights, in Lebesgue spaces, for nonhomogeneous parabolic systems.

Quasilinearization Methods for Nonlinear Parabolic Equations with Functional Dependence

2002 ◽  
Vol 9 (3) ◽  
pp. 431-448
Author(s):  
A. Bychowska
Keyword(s):  
Cauchy Problem ◽  
Parabolic Equations ◽  
Unknown Function ◽  
Functional Dependence ◽  
Nonlinear Parabolic Equations ◽  
Quasilinearization Method ◽  
Convergence Theorems ◽  
Nonlinear Parabolic ◽  
Quasilinearization Methods ◽  
Derivatives Of

Abstract We consider a Cauchy problem for nonlinear parabolic equations with functional dependence. We prove convergence theorems for a general quasilinearization method in two cases: (i) the Hale functional acting only on the unknown function, (ii) including partial derivatives of the unknown function.

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.

Controllability of Semilinear Systems of Parabolic Equations with Delay on the State

2015 ◽  
Vol 17 (6) ◽  
pp. 2105-2114 ◽  
Author(s):  
A. Carrasco ◽  
Hugo Leiva ◽  
N. Merentes ◽  
J. L. Sanchez
Keyword(s):  
Parabolic Equations ◽  
The State ◽  
Semilinear Systems ◽  
Systems Of Parabolic Equations ◽  
Equations With Delay
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