scholarly journals Smooth solutions of parabolic equations with changing time direction

2018 ◽  
Author(s):  
Ivan E. Egorov ◽  
Sergey V. Popov
Keyword(s):  
Parabolic Equations ◽  
Smooth Solutions ◽  
Time Direction

scholarly journals Parabolic equations with changing time direction

2019 ◽  
Author(s):  
Ivan E. Egorov ◽  
Sergey V. Popov
Keyword(s):  
Parabolic Equations ◽  
Time Direction

Solutions in the large for certain nonlinear parabolic equations and applications

1996 ◽  
Vol 126 (1) ◽  
pp. 19-45 ◽  
Author(s):  
Huijiang Zhao ◽  
Changjiang Zhu
Keyword(s):  
Parabolic Equations ◽  
Hyperbolic Conservation Laws ◽  
Parabolic Systems ◽  
Nonlinear Parabolic Equations ◽  
Nonlinear Parabolic Systems ◽  
Smooth Solutions ◽  
Positive Matrix ◽  
Hyperbolic Conservation ◽  
Nonlinear Parabolic ◽  
Nonlinear Hyperbolic Conservation Laws

We prove some results on the global existence of smooth solutions for certain nonlinear parabolic systems of the form Ut + A(U)Ux = DUxx. Here U is a vector and A(U), D are matrices with D a constant, positive matrix. We show how to use our results to study the global continuous (or generalised) solutions to the corresponding nonlinear hyperbolic conservation laws and a conjecture is given.

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