Controllability of Coupled Parabolic Systems with Multiple Underactuations, Part 1: Algebraic Solvability

2019 ◽  
Vol 57 (5) ◽  
pp. 3272-3296 ◽  
Author(s):  
Drew Steeves ◽  
Bahman Gharesifard ◽  
Abdol-Reza Mansouri
Keyword(s):  
Parabolic Systems ◽  
Coupled Parabolic Systems ◽  
Algebraic Solvability

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>

Weighted Gagliardo–Nirenberg Inequalities Involving BMO Norms and Solvability of Strongly Coupled Parabolic Systems

2016 ◽  
Vol 16 (1) ◽  
pp. 125-146 ◽  
Author(s):  
Dung Le
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Parabolic Systems ◽  
Strongly Coupled ◽  
Global Existence Of Solutions ◽  
Coupled Parabolic Systems

AbstractNew weighted Gagliardo–Nirenberg inequalities are introduced together with applications to the local/global existence of solutions to nonlinear strongly coupled and uniform parabolic systems. Much weaker sufficient conditions than those existing in literature for solvability of these systems will be established.

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