Asymptotic and Other Properties of Some Nonlinear Diffusion Models

Abstract

Let Ω ∈ R ³ be a sufficiently smooth bounded fixed domain ensuring the validity of divergence-like theorems and let us consider the initial boundary value problem (i.b.v.p.)

$$ {u_t} = \Delta F(u)\quad (x,t) \in \Omega \times {R^ + } $$

((1))

,

$${u_t} = \left( {x,0} \right) = {u_0}\left( x \right),\quad x \in \Omega$$

((2))

,

$${u_t} = \left( {x,t} \right) = {u_1}\left( x \right),\quad x \in \partial \Omega \times {R^ + }$$

((3))

, where F ∈ C ²(R) and ${u_0} \in C\left( {\overline \Omega } \right)$, u ₁∈ C(∂Ω) are assigned functions.