Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds

• Datum: 2007
• Hauptverfasser: Antoniouk, A. Val., Antoniouk, A. Vict., Антонюк, О. Вал., Антонюк, О. Вік.
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2007
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3404
• Назва журналу: Ukrains’kyi Matematychnyi Zhurnal

We find sufficient conditions on coefficients of diffusion equation on noncompact manifold, that guarantee non-explosion of solutions in a finite time. This property leads to the existence and uniqueness of solutions for corresponding stochastic differential equation with globally non-Lipschitz coe...