Degenerate nonlinear parabolic boundary value problems

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Title 
Degenerate nonlinear parabolic boundary value problems 
Author 
Lin, ChinYuan 
School 
Tulane University 
Academic Field 
Mathematics 
Abstract 
Global existence and uniqueness results are established for mixed initialboundary value problems for degenerate nonlinear parabolic equations of the type ${\partial {\rm u}}\over{\partial {\rm t}}$ = $\phi$(x,$\nabla$u)$\Delta$u + f(x,u,$\nabla$u) where u = u(x,t) is realvalued, x is in a smooth bounded domain $\Omega$ in $\IR\sp{\rm n}$, and t $\geq$ 0. By 'degenerate' we mean that $\phi$(x,$\xi)$ $>$ 0 for x $\epsilon\Omega$ and $\xi\ \epsilon\ \IR\sp{\rm n}$ but possibly $\phi$(x,$\xi)$ = 0 for x $\epsilon\ \partial\ \Omega$. We also consider a variety of boundary conditions, which can be either linear (e.g. Dirichlet, Neumann, Robin or periodic) or nonlinear, in which case it takes the form ${\partial{\rm u}\over\partial{\rm n}}$ $\epsilon$ $\beta$(u(x,t)) for x $\epsilon\ \partial\Omega$, t $\geq$ 0. Here $\nu$ is the unit outer normal to $\partial\Omega$ at x and $\beta$ is a maximal monotone graph in $\IR$ x $\IR$ containing (0,0). In particular, both the equation and the boundary condition can be nonlinear 
Language 
eng 
Advisor(s) 
Goldstein, J. A 
Degree Date 
1987 
Degree 
Ph.D 
Publisher 
Tulane University 
Publication Date 
1987 
Source 
Source: 71 p., Dissertation Abstracts International, Volume: 4905, Section: B, page: 1752 
Identifier 
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Rights 
Copyright is in accordance with U.S. Copyright law 
Contact Information 
acase@tulane.edu 
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