Existence for the thermoelastic thermistor problem

We study a new model for the thermistor problem that consists of a system of dynamic thermoelasticity equations of displacement and a stationary charge conservation equation of electrical current. The heat source generated by Joule heating is quadratic in the gradient of the electrical potential. This system is nonlinear and degenerate since the electrical conductivity is assumed to be temperature dependent and vanishes at large temperatures. We establish the existence of a very weak solution, the so-called “capacity solution” for the model. The proof is based on regularization and time retarding.     

A remark on the thermistor problem with rapidly growing conductivity

A comparison is made between existing results for the stationary thermistor problem. A theorem of existence is given even when the electrical conductivity is a superlinear function of the temperature.     

一类神经网络全局渐近稳定性分析

在这篇文章里,我们研究了一类时滞神经网络的平衡点的存在,唯一性,及其全局渐近稳定性(GA S).我们的主要思想方法是同胚映射,李雅谱诺夫泛函方法,我们在很弱的条件下解决一类时滞神经网络的GA S.     

考虑Joule-Thomson效应的稳态热敏电阻问题

证明考虑Joule-Thomson效应的稳态热敏电阻问题renormalised解的存在性。     

On the stability problem for functional differential equations with infinite delay

We study the stability of functional differential equations with infinite delay, using the Lyapunov functional of constant sign with a derivative of constant sign. Limit equations are constructed in a special phase space. We establish a theorem on localization of a positive limit set and theorems on the stability and the asymptotic stability. The results are illustrated by examples.     

Solvability of the three-dimensional thermistor problem

An existence theorem for one of the complicated versions of the well-known thermistor problem is proved.     

SOME KINDS OF LIAPUNOV FUNCTIONAL IN STABILITY THEORY OF RFDE

ＳＯＭＥＫＩＮＤＳＯＦＬＩＡＰＵＮＯＶＦＵＮＣＴＩＯＮＡＬＩＮＳＴＡＢＩＬＩＴＹＴＨＥＯＲＹＯＦＲＦＤＥＤＵＸＵＥＴＡＮＧ（杜雪堂）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨｕｎａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｃｈａｎｇｓｈａ４１００...     

A heat balance integral solution of the thermistor problem with a modified electrical conductivity

A key driver of thermistor response is a thermally-dependent electrical conductivity. Several variants have been proposed in the literature and it is the purpose of this paper to explore the applicability of a bulk model by way of using the heat balance integral approach to predict the response of a positive temperature coefficient thermistor. Conclusions are presented regarding the sensitivity of the response to electrical conductivity.     

On the existence of periodic solutions in the thermistor problem with degenerate thermal conductivity

Abstract This paper deals with the existence of weak periodic solutions for a parabolic-elliptic system proposed as a model for a time dependent thermistor with degenerate thermal conductivity. Applying the maximal monotone mappings theory, we prove an existence result for weak periodic solutions. Keywords: Nonlinear parabolic-elliptic system of degenerate type, Periodic solutions, Thermistor problem Mathematics Subject Classification (2000): 35B10, 35J60, 35K65     

On solution of the Kostyuchenko problem

Under study is the basis property in L ₂ of a system of Kostyuchenko type. In particular, some criterion is established for the basis property of the Kostyuchenko system under the natural constraints on a parameter in this system.     

某些四阶时滞微分方程解的稳定性

利用Liapunov函数法，得到了一个新的、证明某些四阶非线性时滞微分方程零解渐近稳定的结果．建立结果的限制性条件弱于其他文献给出的的方法．     

具有Kinetic的Muskat问题古典解

考虑了具有Kinetic的多维Muskat问题，并得到了这个问题局部古典解存在唯一性。     

On the canonical solution of indefinite problem with m turning points of even order

We consider the differential equation

(∗)