scholarly journals Global existence for a class of strongly coupled parabolic systems

2005 ◽  
Vol 185 (1) ◽  
pp. 133-154 ◽  
Author(s):  
Dung Le
Keyword(s):  
Global Existence ◽  
Parabolic Systems ◽  
Strongly Coupled ◽  
Coupled Parabolic Systems

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.

Global Existence Results for Near Triangular Nonlinear Parabolic Systems

2013 ◽  
Vol 13 (4) ◽  
Author(s):  
Dung Le
Keyword(s):  
Global Existence ◽  
Weak Solutions ◽  
Parabolic Systems ◽  
Existence Results ◽  
Nonlinear Parabolic Systems ◽  
Strongly Coupled ◽  
Nonlinear Parabolic ◽  
Regularity Of Weak Solutions ◽  
Coupled Parabolic Systems

AbstractWe study the global existence and regularity of weak solutions to strongly coupled parabolic systems whose diffusion matrices are almost triangular.

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>

Über Differenzenverfahren zur numerischen Lösung stark gekoppelter Systeme nichtlinearer Diffusionsgleichungen

1987 ◽  
Vol 42 (10) ◽  
pp. 1133-1140 ◽  
Author(s):  
Karl Graf Finck von Finckenstein
Keyword(s):  
Nonlinear System ◽  
Main Part ◽  
Parabolic Systems ◽  
Difference Operators ◽  
Discrete Approximations ◽  
Strongly Coupled ◽  
One Step ◽  
Difference Methods ◽  
Coupled Parabolic Systems

A class of nonlinear implicit one step difference methods for quasilinear strongly coupled parabolic systems in two space variables is considered. The main part of the paper deals with proving convergence of the discrete approximations for vanishing step sizes. For this purpose, bounds for the inverse difference operators have to be derived previously. This is possible subject to a condition which can be considered as a generalization of the concept “parabolic” to systems. Finally, it is shown that the nonlinear system s arising from the discretizations have one and only one solution for all step sizes being sufficiently small.

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