Some results about blow-up and global existence to a semilinear degenerate heat equation

• Autores: Jacques Giacomoni
• Localización: Revista matemática complutense, ISSN-e 1988-2807, ISSN 1139-1138, Vol. 11, Nº 2, 1998, págs. 325-351
• Idioma: inglés
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• Resumen

  • 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