Maximum dissipation evolution equations for non-linear thermoviscoelasticity

1999 ◽  
Vol 34 (2) ◽  
pp. 361-385 ◽  
Author(s):  
Henry W. Haslach ◽  
Nianning Zeng
Keyword(s):  
Evolution Equations ◽  
Non Linear ◽  
Linear Thermoviscoelasticity

scholarly journals A direct algorithm of exp-function method for non-linear evolution equations in fluids

2016 ◽  
Vol 20 (3) ◽  
pp. 881-884 ◽  
Author(s):  
Sheng Zhang ◽  
Jiahong Li ◽  
Luyao Zhang
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Mathematical Tool ◽  
Direct Algorithm ◽  
Linear Evolution ◽  
Non Linear ◽  
De Vries ◽  
Linear Evolution Equations

In this paper, a direct algorithm of the exp-function method is proposed for exactly solving non-linear evolution equations. To illustrate the validity and advantages of the algorithm, the Korteweg-de Vries and Jimbo-Miwa equations are considered. As a result, exact solutions are obtained. It is shown that the exp-function method with the direct algorithm provides a simpler but effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.

scholarly journals A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations

2020 ◽  
Vol 32 (1) ◽  
pp. 59-88
Author(s):  
STANISŁAW MIGÓRSKI ◽  
WEIMIN HAN ◽  
SHENGDA ZENG
Keyword(s):  
Dynamical System ◽  
Evolution Equations ◽  
Frictional Contact ◽  
Maximal Monotone ◽  
Contact Boundary ◽  
Hemivariational Inequalities ◽  
Response Condition ◽  
Linear Evolution ◽  
Linear Evolution Equation ◽  
Non Linear

The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

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