scholarly journals AN EXISTENCE RESULT FOR QUASILINEAR PARABOLIC SYSTEMS WITH LOWER ORDER TERMS

2021 ◽  
Vol 26 (4) ◽  
pp. 669-683
Author(s):  
Farah Balaadich ◽  
Elhoussine Azroul
Keyword(s):  
Existence Result ◽  
Parabolic Systems ◽  
Young Measures ◽  
Open Domain ◽  
Existence Of Weak Solutions ◽  
Quasilinear Parabolic Systems ◽  
Lower Order Terms ◽  
Galerkin’S Approximation ◽  
Quasilinear Parabolic ◽  
Diffusion Problems

In this paper we prove the existence of weak solutions for a class of quasilinear parabolic systems, which correspond to diffusion problems, in the form where Ω is a bounded open domain of be given and The function v belongs to is in a moving and dissolving substance, the dissolution is described by f and the motion by g. We prove the existence result by using Galerkin’s approximation and the theory of Young measures.

Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method

2017 ◽  
Vol 29 (5) ◽  
pp. 1039-1064 ◽  
Author(s):  
Arina A. Arkhipova ◽  
Jana Stará
Keyword(s):  
Approximation Method ◽  
Weak Solutions ◽  
Parabolic Systems ◽  
John 1 ◽  
Quasilinear Parabolic Systems ◽  
Regularity Of Weak Solutions ◽  
Divergence Type ◽  
Quasilinear Parabolic

AbstractWe prove a modification of the so-called A(t)-caloric lemma stated in our earlier work with O. John [1] to study regularity of weak solutions to parabolic systems of non-divergence type with non-smooth in time principal matrices. As an application, we prove smoothness results in Morrey and Campanato spaces for linear parabolic systems of non-divergence type by the A(t)-caloric approximation method.

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