On the behavior of solutions to the Cauchy problem for nonlinear degenerate parabolic systems with large time values

1995 ◽  
Vol 57 (1) ◽  
pp. 28-33
Author(s):  
A. V. Vlaskin
Keyword(s):  
Cauchy Problem ◽  
Large Time ◽  
Parabolic Systems ◽  
The Cauchy Problem ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Nonlinear Degenerate

scholarly journals Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Na Wei ◽  
Xiangyu Ge ◽  
Yonghong Wu ◽  
Leina Zhao
Keyword(s):  
Weak Solutions ◽  
Vector Fields ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Lp Estimates ◽  
Reverse Hölder Inequalities ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Reverse Hölder ◽  
Nonlinear Degenerate

This paper is devoted to the Lp estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the Lp estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.

scholarly journals A degenerate parabolic–hyperbolic Cauchy problem with a stochastic force

2015 ◽  
Vol 12 (03) ◽  
pp. 501-533 ◽  
Author(s):  
Caroline Bauzet ◽  
Guy Vallet ◽  
Petra Wittbold
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Stochastic Forcing ◽  
Hyperbolic Problem ◽  
Stochastic Force ◽  
The Cauchy Problem ◽  
Degenerate Parabolic ◽  
Entropy Formulation ◽  
Uniqueness Of A Solution ◽  
Nonlinear Degenerate

In this paper, we are interested in the Cauchy problem for a nonlinear degenerate parabolic–hyperbolic problem with multiplicative stochastic forcing. Using an adapted entropy formulation a result of existence and uniqueness of a solution is proven.

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