Nonexplosion and solvability of nonlinear diffusion equations on noncompact manifolds |
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Authors: | A. Val. Antonyuk A. Vik. Antonyuk |
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Affiliation: | (1) Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine |
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Abstract: | We find sufficient conditions for the coefficients of a diffusion equation on a noncompact manifold that guarantee the nonexplosion of solutions in finite time. This property leads to the existence and uniqueness of solutions for the corresponding stochastic differential equation with globally non-Lipschitz coefficients. Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1454–1472, November, 2007. |
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