Nonlinear parabolic equations with natural growth terms and measure initial data

• Dominique Blanchard ^[1] ; Alessio Porretta ^[2]
  1. [1] University of Rouen

     University of Rouen

     Arrondissement de Rouen, Francia

     
  2. [2] Università di Roma II, Italy
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 30, Nº 3-4, 2001, págs. 583-622
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • We investigate the existence and the stability of the solutions of a nonlinear evolution equation with a local quadratic term with respect to the gradient of the type g(u)|Du|2 and for measure initial data. We extend the notion of renormalized solutions for this problem. Under a natural condition on the convergence of the initial data, we prove the compactness of the truncation of solutions in the energy space. Then we show that the integrability of g at infinity is a necessary and sufficient condition for the stability of the problem with respect to general measure data, as well as for the existence of renormalized solutions.