In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations...In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations involving nonconvex energies.展开更多
This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given...The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.展开更多
§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if...§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if展开更多
In this study,we propose that many different thermodynamic modeling approaches,including the general equation for the non-equilibrium reversible–irreversible coupling(GENERIC),Onsager’s variational principle,the ene...In this study,we propose that many different thermodynamic modeling approaches,including the general equation for the non-equilibrium reversible–irreversible coupling(GENERIC),Onsager’s variational principle,the energetic variational approach,and classical irreversible thermodynamics,can all be cast into the gradient-conservative structure(GCS).GCS enjoys many nice mathematical properties,has close connection with the large deviations principle and gradient flows in Wasserstein space,and fulfills laws of thermodynamics.Our results demonstrate that the GCS may serve as a unified theoretical framework to model various non-equilibrium thermodynamic processes.展开更多
文摘In this paper, we establish the existence of solutions for gradient systems ofevolution under some type （M） and semi-coerciveness conditions. The main result is appliedin order to solve nonlinear diffusion equations involving nonconvex energies.
文摘This paper deals with an abstract periodic gradient system in which the gradient is taken with respect to a variable metric. We obtain an existence and uniqueness result via the application of a global inverse theorem.
基金supported by the National Natural Science Foundation of China(No.11972241)the Natural Science Foundation of Jiangsu Province (No.BK20191454)the Scientific Research Foundation of Suzhou University of Science and Technology (No.XKZ2017005)。
文摘The combined gradient representations for generalized Birkhoffian systems in event space are studied.Firstly,the definitions of six kinds of combined gradient systems and corresponding differential equations are given.Secondly,the conditions under which generalized Birkhoffian systems become combined gradient systems are obtained. Finally,the characteristics of combined gradient systems are used to study the stability of generalized Birkhoffian systems in event space. Seven examples are given to illustrate the results.
文摘§1. Introduction In this paper we consider the parabolic system (?)t/(?)ui-div(|▽u|p-2▽ui)=0(1≤i≤m), with p>1, where ui=ui(x, t), ▽=gradxand x varies in an open domain Ω(?)RN. The system is degenerate if p>2 or singular if 1<p<2. A vector function u=(u1, u2, …, um) defined in ΩT=Ω×[0, T] is called a solution of the system (1.1) if
基金supported by the National Natural Science Foundation of China(12205135)Guangdong Basic and Applied Basic Research Foundation(2023A1515010157)the Natural Science Foundation of Fujian Province of China(2024J01212).
文摘In this study,we propose that many different thermodynamic modeling approaches,including the general equation for the non-equilibrium reversible–irreversible coupling(GENERIC),Onsager’s variational principle,the energetic variational approach,and classical irreversible thermodynamics,can all be cast into the gradient-conservative structure(GCS).GCS enjoys many nice mathematical properties,has close connection with the large deviations principle and gradient flows in Wasserstein space,and fulfills laws of thermodynamics.Our results demonstrate that the GCS may serve as a unified theoretical framework to model various non-equilibrium thermodynamic processes.
