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
2020 ◽  
Vol 28 (6) ◽  
pp. 797-814
Author(s):  
Elena-Alexandra Melnig

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.


2002 ◽  
Vol 9 (3) ◽  
pp. 431-448
Author(s):  
A. Bychowska

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.


Author(s):  
K. Azelmat ◽  
M. Kbiri Alaoui ◽  
D. Meskine ◽  
A. Souissi

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


Author(s):  
Haifeng Shang

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.


2013 ◽  
Vol 24 (03) ◽  
pp. 427-464 ◽  
Author(s):  
CRISTIAN MORALES-RODRIGO ◽  
J. IGNACIO TELLO

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.


2015 ◽  
Vol 17 (6) ◽  
pp. 2105-2114 ◽  
Author(s):  
A. Carrasco ◽  
Hugo Leiva ◽  
N. Merentes ◽  
J. L. Sanchez

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