Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
Gliklikh, Yuri E. (2006)
Abstract and Applied Analysis
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Displaying similar documents to “On the notion of -completeness of a stochastic flow on a manifold.”
Necessary and sufficient conditions for global-in-time existence of solutions of ordinary, stochastic, and parabolic differential equations.
Conditions for global existence of solutions of ordinary differential, stochastic differential, and parabolic equations.
Gliklikh, Yuri E., Morozova, Lora A. (2004)
International Journal of Mathematics and Mathematical Sciences
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An operator theoretic approach to stochastic flows on manifolds
David Applebaum (1992)
Séminaire de probabilités de Strasbourg
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Controlling the stochastic sensitivity in thermochemical systems under incomplete information
Irina Bashkirtseva (2018)
Kybernetika
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Complex dynamic regimes connected with the noise-induced mixed-mode oscillations in the thermochemical model of flow reactor are studied. It is revealed that the underlying reason of such excitability is in the high stochastic sensitivity of the equilibrium. The problem of stabilization of the excitable equilibrium regimes is investigated. We develop the control approach using feedback regulators which reduce the stochastic sensitivity and keep the randomly forced system near the stable...
The statistical equilibrium of an isotropic stochastic flow with negative Lyapounov exponents is trivial
Richard W. R. Darling, Yves Le Jan (1988)
Séminaire de probabilités de Strasbourg
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On the -instability of fluid flows
Alexander Shnirelman (1999-2000)
Séminaire Équations aux dérivées partielles
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On differential equations and inclusions with mean derivatives on a compact manifold
S.V. Azarina, Yu.E. Gliklikh (2007)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.
A convergence result for the Gradient Flow of ∫ |A| 2 in Riemannian Manifolds
Annibale Magni (2015)
Geometric Flows
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We study the gradient flow of the L2−norm of the second fundamental form for smooth immersions of two-dimensional surfaces into compact Riemannian manifolds. By analogy with the results obtained in [10] and [11] for the Willmore flow, we prove lifespan estimates in terms of the L2−concentration of the second fundamental form of the initial data and we show the existence of blowup limits. Under special condition both on the initial data and on the target manifold, we prove a long time...
Positivity theorem for a general manifold.
Rémi Léandre (2005)
SORT
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We give a generalization in the non-compact case to various positivity theorems obtained by Malliavin Calculus in the compact case.
On the -instability and -controllability of steady flows of an ideal incompressible fluid
Alexander Shnirelman (1999)
Journées équations aux dérivées partielles
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In the existing stability theory of steady flows of an ideal incompressible fluid, formulated by V. Arnold, the stability is understood as a stability with respect to perturbations with small in vorticity. Nothing has been known about the stability under perturbation with small energy, without any restrictions on vorticity; it was clear that existing methods do not work for this (the most physically reasonable) class of perturbations. We prove that in fact, every nontrivial steady...