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We consider the following nonlinear system of parabolic equations: (1) ut =?u???(u?v), ?vt =?v+u?av for x?B R, t> 0. Here ?,? and a are positive constants and BR is a ball of radius R> 0 in R2. At the boundary of BR, we impose homogeneous Neuma[...]texto impreso
Arrieta Algarra, José María ; Rodríguez Bernal, Aníbal ; Souplet, Philippe | Scuola Normale Superiore | 2004We consider a one-dimensional semilinear parabolic equation with a gradient nonlinearity. We provide a complete classification of large time behavior of the classical solutions u: either the space derivative u., blows up in finite time (with u i[...]texto impreso
This paper concerns the Cauchy problem ut?uxx=up, x?R, t> 0, u(x,0)=u0(x), x?R, where p> 1 and u0(x) is a continuous, nonnegative and bounded function. It has been previously proved that if x=x¯, t=T is a blow-up point, then there are three case[...]texto impreso
The subject of this paper is the study of a free boundary problem for a steady fluid flow through a porous medium, in which the classical Darcy law (1) ?!v = ar(p(x)+xn), x = (x1, · · · , xn) 2 Rn, a > 0, is replaced by the nonlinear law (2) |?[...]
