Unspecified Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: http://doi.org/10.5167/uzh-22758 Originally published at: Chipot, M; Fila, M; Quittner, P (1991).… Expand

it is well known that there exist choices of u0 for which the corresponding solutions tend to zero as t -+ cc and other choices for which the solutions blow up in finite time. If we are interested in… Expand

In this paper, we consider the system u t = u, v t = v x 2R N , t > 0, @u @x 1 = v p , @v @x 1 = u q x 1 = 0, t > 0, u(x, 0) = u 0 (x), v(x, 0) = v 0 (x) x2R N , where R N = {(x 1 ,x 0 ) | x 0 2 R N… Expand

Abstract. We derive results on blow-up rates for parabolic
equations and systems from Fujita-type theorems. We complement a
previous study by allowing (possibly unbounded) domains with boundary.

We study the behavior of solutions of the Cauchy problem for a diffusion equation with supercritical nonlinearity. It is shown that if two solutions are initially close enough near the spatial… Expand

In this paper positive solutions of the heat equation with a nonlinear Neumann boundary conditions in an upper halfspace are studied. The optimal result on blow-up rate, valid for all solutions which… Expand