scholarly journals Global and Blow-Up Solutions for Nonlinear Degenerate Parabolic Systems with Crosswise-Diffusion

2000 ◽  
Vol 244 (2) ◽  
pp. 263-278 ◽  
Author(s):  
Zhi-wen Duan ◽  
Li Zhou
Keyword(s):  
Blow Up ◽  
Parabolic Systems ◽  
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.

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