Resumen de Some results about blow-up and global existence to a semilinear degenerate heat equation
In this paper, we are dealing with the following degenerate parabolic problem: (Pt) { ¶tu - |x|2Du = g(u) in R+ ¿B1 u(t,x)º 0 in R+¿¶ B1; u(0,x) = u0³ 0 where B1={x Î RN; ||x||=1} and g is nonlinear.
We are interested in analizying such questions as local and global existence, blow-up in finite time and convergence to a stationary solution for solutions of (Pt).
First, we give some examples of nonlinearities g where the blow up in L2(dx/|x|2) ÇLµ (B1) occurs. In a second part of this work, we present two cases of global existence of solutions to (Pt) which converge in Lµ (B1) to a stationary solution of (Pt) when
