Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds

• Published in: Український математичний журнал
• Date: 2007
• ISSN: 1027-3190
• Main Authors: Antoniouk, A.Val., Antoniouk, A.Vict.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2007
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/172504
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds / A.Val. Antoniouk, A.Vict. Antoniouk // Український математичний журнал. — 2007. — Т. 59, № 11. — С. 1454–1472. — Бібліогр.: 13 назв. — англ.

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 coef...