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A density dependent diffusion equation in population dynamics: stabilization to equilibrium. (English) Zbl 0607.35052

The authors consider the problem \[ u_ t=\Delta \phi (u)+div(u\nabla v)\quad in\quad \Omega \times {\mathbb{R}}^+ \]
\[ (\partial /\partial n)\phi (u)+u\partial v/\partial n=0\quad on\quad \delta \Omega \times {\mathbb{R}}^+;\quad u(x,0)=u_ 0(x). \] It is assumed that the smooth function \(\phi\) (s) satisfies \(\phi (0)=0\), \(\phi '(0)=0\) and \(\phi '(s)>0\) for \(s>0.\)
They discuss the large time behavior of u as well as existence, regularity and uniqueness of solutions.
Reviewer: R.Sperb

MSC:

35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35K65 Degenerate parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
92D25 Population dynamics (general)
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