On the regularity of weak solutions to parabolic systems in two spatial dimensions

1998 ◽  
Vol 23 (7-8) ◽  
pp. 437-451 ◽  
Author(s):  
Oldiichi John ◽  
Jana Stará
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Regularity Of Weak Solutions ◽  
Spatial Dimensions

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.

Global Existence Results for Near Triangular Nonlinear Parabolic Systems

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Dung Le
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
Parabolic Systems ◽  
Existence Results ◽  
Nonlinear Parabolic Systems ◽  
Strongly Coupled ◽  
Nonlinear Parabolic ◽  
Regularity Of Weak Solutions ◽  
Coupled Parabolic Systems

AbstractWe study the global existence and regularity of weak solutions to strongly coupled parabolic systems whose diffusion matrices are almost triangular.

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