Estimates from below for unbounded solutions of a quasilinear parabolic system of equations

1990 ◽  
Vol 47 (2) ◽  
pp. 111-116
Author(s):  
V. A. Galaktionov ◽  
S. A. Posashkov
Keyword(s):  
Parabolic System ◽  
System Of Equations ◽  
Quasilinear Parabolic System ◽  
Unbounded Solutions ◽  
Quasilinear Parabolic ◽  
Parabolic System Of Equations

Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Karoline Disser
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Well Posedness ◽  
System Of Equations ◽  
Quasilinear Parabolic System ◽  
Interface Diffusion ◽  
Quasilinear Parabolic ◽  
Parabolic System Of Equations

AbstractIn this paper, we consider a quasilinear parabolic system of equations describing coupled bulk and interface diffusion, including mixed boundary conditions. The setting naturally includes non-smooth domains Ω. We show local well-posedness using maximal

scholarly journals A PLANKTON ALLELOPATHIC MODEL DESCRIBED BY A DELAYED QUASILINEAR PARABOLIC SYSTEM

2012 ◽  
Vol 17 (4) ◽  
pp. 485-497 ◽  
Author(s):  
Canrong Tian ◽  
Peng Zhu
Keyword(s):  
Parabolic System ◽  
Upper And Lower Solutions ◽  
Asymptotically Stable ◽  
Stability Of Solutions ◽  
Quasilinear Parabolic System ◽  
Monotone Iterations ◽  
Engineering Problems ◽  
Existence And Stability ◽  
Uniform Equilibrium ◽  
Quasilinear Parabolic

The quasilinear parabolic system has been applied to a variety of physical and engineering problems. However, most works lack effective techniques to deal with the asymptotic stability. This paper is concerned with the existence and stability of solutions for a plankton allelopathic model described by a quasilinear parabolic system, in which the diffusions are density-dependent. By the coupled upper and lower solutions and its associated monotone iterations, it is shown that under some parameter conditions the positive uniform equilibrium is asymptotically stable. Some biological interpretations for our results are given.

scholarly journals On some classes of coefficient inverse problems for parabolic systems of equations with the ovedetermination date of evolutionary type

2015 ◽  
Vol 11 (3) ◽  
pp. 51-57
Author(s):  
Ekaterina M Korotkova
Keyword(s):  
Inverse Problems ◽  
Parabolic System ◽  
Local Existence ◽  
Parabolic Systems ◽  
System Of Equations ◽  
Systems Of Equations ◽  
Local Existence Theorem ◽  
Coefficient Inverse Problems ◽  
Boundary Operators ◽  
Parabolic System Of Equations

The article is devoted to the question of wellposedness in the Sobolev spaces of inverse problems on determining the righthand side and coefficients in a parabolic system of equations. The overdetermination conditions are the values of a part of the vector of solutions on some system of surfaces. Under special conditions on the boundary operators the local existence theorem of solutions to the problem is established.

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