Bertsch, M.; Hilhorst, D. A density dependent diffusion equation in population dynamics: stabilization to equilibrium. (English) Zbl 0607.35052 SIAM J. Math. Anal. 17, 863-883 (1986). 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 Cited in 22 Documents 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) Keywords:diffusion; stationary solutions; Lyapunov functional; population dynamics; large time behavior; existence; regularity; uniqueness PDFBibTeX XMLCite \textit{M. Bertsch} and \textit{D. Hilhorst}, SIAM J. Math. Anal. 17, 863--883 (1986; Zbl 0607.35052) Full Text: DOI