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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Entropy-Dissipation Informed Neural Networks for McKean-Vlasov type PDEs
McKean-Vlasov型 偏微分方程 熵耗散 信息神经网络
2023/4/13
We extend the concept of self-consistency for the Fokker-Planck equation (FPE) [Shen et al., 2022] to the more general McKean-Vlasov equation (MVE). While FPE describes the macroscopic behavior of par...
Entropy and Renormalized Solutions for the p(x)-Kaokacuab Equation with Measure Data
Variable exponents Entropy solutions Renormalized solutions Exist- ence Uniqueness
2015/5/4
In this paper we prove the existence and uniqueness of both entropy solutions and renormalized solutions for the p(x)-Laplacian equation with variable exponents and a signed measure in L 1 (Ω) +...
Time relaxation of a phase-field model with entropy balance
phase-field model entropy balance Analysis of PDEs
2011/9/14
Abstract: We deal with a system of two coupled differential equations, describing the evolution of a first order phase transition. In particular, we have two non-linear parabolic equations: the first ...
Research Note on a Parabolic Heat-Balance Integral Method with Unspecified Exponent: An Entropy Generation Approach in Optimal Profile Determination
Research Note on a Parabolic Heat-Balance Integral Method Unspecified Exponent Entropy Generation Optimal Profile Determination
2011/1/20
The heat-bal ance in te gral method of Good man is stud ied with two sim ple 1-D heat con duc tion prob lems with pre scribed tem per a ture and flux bound ary con di tions.These clas si cal prob lems...
Entropy power inequality for a family of discrete random variables
Entropy power inequality family of discrete random variables
2011/1/17
It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds wit...
The Entropy Conjecture for Diffeomorphisms away from Tangencies
Entropy conjecture principal symbolic extensions
2011/1/17
We prove that every C1 diffeomorphism away from homoclinic tangencies is entropy expansive, with locally uniform expansivity constant.Consequently, such diffeomorphisms satisfy Shub’s entropy conjectu...
Entropy Solutions for a Non-Uniformly Parabolic Equation
Entropy solutions Existence Uniqueness Parabolic
2015/5/4
In this paper we prove the existence and uniqueness of entropy solutions for the initial-boundary value problem of a non-uniformly parabolic equation. Moreover, we establish a comparison result. Some ...
Renormalized and Entropy Solutions for Nonlinear Parabolic Equations with Variable Exponents and L1 Data
Variable exponents Renormalized solutions Entropy solutions Exist- ence Uniqueness
2015/5/4
Abstract. In this paper we prove the existence and uniqueness of both renormalized solutions and entropy solutions for nonlinear parabolic equations with variable exponents and L 1 data. And moreover,...