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Author : Chuanqiang Chen
Release : 2019
Genre :
Kind : eBook
Book Rating : 438/5 ( reviews)
Book Synopsis On Space-time Quasiconcave Solutions of the Heat Equation by : Chuanqiang Chen
Download or read book On Space-time Quasiconcave Solutions of the Heat Equation written by Chuanqiang Chen. This book was released on 2019. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chuanqiang Chen
Release : 2019-06-10
Genre : Heat equation
Kind : eBook
Book Rating : 241/5 ( reviews)
Book Synopsis On Space-Time Quasiconcave Solutions of the Heat Equation by : Chuanqiang Chen
Download or read book On Space-Time Quasiconcave Solutions of the Heat Equation written by Chuanqiang Chen. This book was released on 2019-06-10. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.
Author : Massimiliano Berti
Release : 2020-04-03
Genre : Education
Kind : eBook
Book Rating : 695/5 ( reviews)
Book Synopsis Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves by : Massimiliano Berti
Download or read book Quasi-periodic Standing Wave Solutions of Gravity-Capillary Water Waves written by Massimiliano Berti. This book was released on 2020-04-03. Available in PDF, EPUB and Kindle. Book excerpt: The authors prove the existence and the linear stability of small amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean with infinite depth under the action of gravity and surface tension. Such an existence result is obtained for all the values of the surface tension belonging to a Borel set of asymptotically full Lebesgue measure.
Author : Luigi Ambrosio
Release : 2020-02-13
Genre : Education
Kind : eBook
Book Rating : 131/5 ( reviews)
Book Synopsis Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces by : Luigi Ambrosio
Download or read book Nonlinear Diffusion Equations and Curvature Conditions in Metric Measure Spaces written by Luigi Ambrosio. This book was released on 2020-02-13. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this paper is to provide new characterizations of the curvature dimension condition in the context of metric measure spaces (X,d,m). On the geometric side, the authors' new approach takes into account suitable weighted action functionals which provide the natural modulus of K-convexity when one investigates the convexity properties of N-dimensional entropies. On the side of diffusion semigroups and evolution variational inequalities, the authors' new approach uses the nonlinear diffusion semigroup induced by the N-dimensional entropy, in place of the heat flow. Under suitable assumptions (most notably the quadraticity of Cheeger's energy relative to the metric measure structure) both approaches are shown to be equivalent to the strong CD∗(K,N) condition of Bacher-Sturm.
Author : Tvrtko Tadić
Release : 2019-12-02
Genre : Education
Kind : eBook
Book Rating : 85X/5 ( reviews)
Book Synopsis Time-Like Graphical Models by : Tvrtko Tadić
Download or read book Time-Like Graphical Models written by Tvrtko Tadić. This book was released on 2019-12-02. Available in PDF, EPUB and Kindle. Book excerpt: The author studies continuous processes indexed by a special family of graphs. Processes indexed by vertices of graphs are known as probabilistic graphical models. In 2011, Burdzy and Pal proposed a continuous version of graphical models indexed by graphs with an embedded time structure— so-called time-like graphs. The author extends the notion of time-like graphs and finds properties of processes indexed by them. In particular, the author solves the conjecture of uniqueness of the distribution for the process indexed by graphs with infinite number of vertices. The author provides a new result showing the stochastic heat equation as a limit of the sequence of natural Brownian motions on time-like graphs. In addition, the author's treatment of time-like graphical models reveals connections to Markov random fields, martingales indexed by directed sets and branching Markov processes.
