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.

scholarly journals A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hong Liu ◽  
Haihua Lu
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Parabolic System ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Dirichlet Boundary Conditions ◽  
Nonlocal Sources ◽  
Semilinear Parabolic System ◽  
Semilinear Parabolic ◽  
Existence Criteria

We investigate the positive solutions of the semilinear parabolic system with coupled nonlinear nonlocal sources subject to weighted nonlocal Dirichlet boundary conditions. The blow-up and global existence criteria are obtained.

LIPSCHITZ CONTINUITY FOR H-CONVEX FUNCTIONS IN CARNOT GROUPS

2006 ◽  
Vol 08 (01) ◽  
pp. 1-8 ◽  
Author(s):  
MINGBAO SUN ◽  
XIAOPING YANG
Keyword(s):  
Convex Functions ◽  
Lipschitz Continuity ◽  
Carnot Group ◽  
Carnot Groups ◽  
Lipschitz Continuous ◽  
Locally Lipschitz ◽  
Locally Lipschitz Continuous

For a Carnot group G of step two, we prove that H-convex functions are locally bounded from above. Therefore, H-convex functions on a Carnot group G of step two are locally Lipschitz continuous by using recent results by Magnani.

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