Global Existence and Finite Time Blowup

2021 ◽  
pp. 131-164
Author(s):  
Mingxin Wang
Keyword(s):  
Global Existence ◽  
Finite Time ◽  
Finite Time Blowup ◽  
Time Blowup

scholarly journals Blowup of Solutions to the Compressible Euler-Poisson and Ideal MHD Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Wenming Hu
Keyword(s):  
Finite Time ◽  
Euler System ◽  
Time Dependent ◽  
Poisson System ◽  
Blowup Of Solutions ◽  
Finite Time Blowup ◽  
Ideal Mhd ◽  
Compressible Euler ◽  
Time Blowup

In the present paper, we study the blowup of the solutions to the full compressible Euler system and pressureless Euler-Poisson system with time-dependent damping. By some delicate analysis, some Riccati-type equations are achieved, and then, the finite time blowup results can be derived.

scholarly journals A diffusion equation with localized chemical reactions

1994 ◽  
Vol 37 (1) ◽  
pp. 101-118 ◽  
Author(s):  
John M. Chadam ◽  
Hong-Ming Yin
Keyword(s):  
Global Existence ◽  
Diffusion Equation ◽  
Finite Time ◽  
Diffusion Processes ◽  
Model Problem ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Well Posedness ◽  
Blowup Rate ◽  
Time Blowup

In some chemical reaction–diffusion processes, the reaction takes place only at some local sites, due to the presence of a catalyst. In this paper we study the well-posedness of a model problem of this type. Sufficient conditions are found to ensure global existence and finite time blowup. The blowup rate and the blowup set are also investigated in the case of special nonlinearity.

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