scholarly journals Simultaneous and non-simultaneous quenching for a coupled semilinear parabolic system in a $ n $-dimensional ball with singular localized sources

2021 ◽  
Vol 6 (7) ◽  
pp. 7704-7718
Author(s):  
W. Y. Chan ◽  
Keyword(s):  
Parabolic System ◽  
Semilinear Parabolic System ◽  
Dimensional Ball ◽  
Semilinear Parabolic ◽  
Localized Sources

Über die C2-Kompaktheit der Bahn von Lösungen semflinearer parabolischer Systeme

1982 ◽  
Vol 93 (1-2) ◽  
pp. 99-103 ◽  
Author(s):  
Reinhard Redlinger
Keyword(s):  
Boundary Conditions ◽  
Regular Solution ◽  
Parabolic System ◽  
Lipschitz Continuous ◽  
Semilinear Parabolic System ◽  
Locally Lipschitz ◽  
Semilinear Parabolic ◽  
Locally Lipschitz Continuous

SynopsisThe semilinear parabolic systemut+A(x, D)u=g(u) in (0, ∞) × Ω, Ω⊂ℝnbounded,u∈ ℝN, with homogeneous boundary conditionsB(x, D)u=0 on (0, ∞)×∂Ω is considered. The non-linearitygis assumed to be locally Lipschitz-continuous. It is shown that the orbit of a bounded regular solutionuis relatively compact in.

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