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The mixed boundary value problem for degenerate quasilinear parabolic equations

Authors:

Chen Zuchi Qian Chunlin

Institution:

1. University of Science and Technology of China, China

Abstract:

Let Ω⊂R ⁿ(n≥2) be a bounded open set;Q _T=Ω×0,T],S _T=δΩ×0,T],S ₁,S ₂ be the partial boundaries of Ω andS ₁∪S ₂=δΩ,S ₁∩S ₂=Φ. We denote Γ_1.T=S ₁×0,T], Γ_2.T=S ₂×0,T], and consider the problem

$\left\{ \begin{gathered} u_t - \frac{\partial }{{\partial x_1 }}a_i (x,t,u,u_x ) + a(x,t,u,u_x ) = f(x,t),(x,t) \in Q_{T,} \hfill \\ \sum\limits_{i = 1}^m {a_i (x,t,u,u_x } )\cos (\vec n,x_i ) = \psi (x,t),(x,t) \in \Gamma _{1.T} , \hfill \\ u(x,t) = 0,(x,t) \in \Gamma _{1.T} , \hfill \\ u(x,0) = \psi _0 (x),x \in \Omega \hfill \\ \end{gathered} \right.$

Keywords:
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