Quasilinear Parabolic Systems with Mixed Boundary Conditions on Nonsmooth Domains

2008 ◽  
Vol 40 (1) ◽  
pp. 292-305 ◽  
Author(s):  
Matthias Hieber ◽  
Joachim Rehberg
Keyword(s):  
Boundary Conditions ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Parabolic Systems ◽  
Quasilinear Parabolic Systems ◽  
Nonsmooth Domains ◽  
Quasilinear Parabolic

Well-posedness for coupled bulk-interface diffusion with mixed boundary conditions

Analysis ◽  
2015 ◽  
Vol 35 (4) ◽  
Author(s):  
Karoline Disser
Keyword(s):  
Boundary Conditions ◽  
Parabolic System ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Well Posedness ◽  
System Of Equations ◽  
Quasilinear Parabolic System ◽  
Interface Diffusion ◽  
Quasilinear Parabolic ◽  
Parabolic System Of Equations

AbstractIn this paper, we consider a quasilinear parabolic system of equations describing coupled bulk and interface diffusion, including mixed boundary conditions. The setting naturally includes non-smooth domains Ω. We show local well-posedness using maximal

PARTIAL DIFFERENTIAL EQUATIONS OF ELLIPTIC TYPE IN NONSMOOTH DOMAINS

2005 ◽  
Vol 07 (06) ◽  
pp. 787-808
Author(s):  
HELDER CANDIDO RODRIGUES
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence Result ◽  
Critical Case ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Elliptic Type ◽  
Nonsmooth Domains ◽  
Definition Of

This paper studies the problem -Δu + λu = up in nonsmooth domains with mixed boundary conditions. Special attention will be given here to the critical case and to domains which have no further regularity than a Lipschitzian boundary. For such domains, we obtain a generalized version of Cherrier's inequality and prove an existence result. This was achieved by using an extended definition of the manifold.

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