Life span of solutions with large initial data for a class of coupled parabolic systems

2012 ◽  
Vol 64 (3) ◽  
pp. 705-717 ◽  
Author(s):  
Xiaojing Xu ◽  
Zhuan Ye
Keyword(s):  
Initial Data ◽  
Life Span ◽  
Parabolic Systems ◽  
Large Initial Data ◽  
Coupled Parabolic Systems

scholarly journals Life span of solutions with large initial data for a semilinear parabolic system coupling exponential reaction terms

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sen Zhou
Keyword(s):  
Lower Bound ◽  
Initial Data ◽  
Life Span ◽  
Parabolic Equations ◽  
Coupled Systems ◽  
Large Initial Data ◽  
Semilinear Parabolic System ◽  
Systems Of Parabolic Equations ◽  
System Coupling ◽  
Semilinear Parabolic

Abstract In this paper, we study a coupled systems of parabolic equations subject to large initial data. By using comparison principle and Kaplan’s method, we get the upper and lower bound for the life span of the solutions.

scholarly journals Lorentz spaces in action on pressureless systems arising from models of collective behavior

2021 ◽  
Author(s):  
Raphaël Danchin ◽  
Piotr Bogusław Mucha ◽  
Patrick Tolksdorf
Keyword(s):  
Initial Data ◽  
Collective Behavior ◽  
Existence And Uniqueness ◽  
Maximal Regularity ◽  
Parabolic Systems ◽  
Lorentz Spaces ◽  
Regularity Estimate ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Time Existence

AbstractWe are concerned with global-in-time existence and uniqueness results for models of pressureless gases that come up in the description of phenomena in astrophysics or collective behavior. The initial data are rough: in particular, the density is only bounded. Our results are based on interpolation and parabolic maximal regularity, where Lorentz spaces play a key role. We establish a novel maximal regularity estimate for parabolic systems in $$L_{q,r}(0,T;L_p(\Omega ))$$ L q , r ( 0 , T ; L p ( Ω ) ) spaces.

scholarly journals Global existence and nonexistence for a class of finitely degenerate coupled parabolic systems with high initial energy level

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yuxuan Chen ◽  
Jiangbo Han
Keyword(s):  
Energy Level ◽  
Global Existence ◽  
Blow Up ◽  
Parabolic Systems ◽  
Initial Energy ◽  
Blowup Time ◽  
Positive Initial Energy ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Coupled Parabolic Systems

<p style='text-indent:20px;'>In this paper, we consider a class of finitely degenerate coupled parabolic systems. At high initial energy level <inline-formula><tex-math id="M1">\begin{document}$ J(u_{0})&gt;d $\end{document}</tex-math></inline-formula>, we present a new sufficient condition to describe the global existence and nonexistence of solutions for problem (1)-(4) respectively. Moreover, by applying the Levine's concavity method, we give some affirmative answers to finite time blow up of solutions at arbitrary positive initial energy <inline-formula><tex-math id="M2">\begin{document}$ J(u_{0})&gt;0 $\end{document}</tex-math></inline-formula>, including the estimate of upper bound of blowup time.</p>

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