Displaying 1061 – 1080 of 1233

Showing per page

Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity

Olaf Klein (2004)

Applications of Mathematics

The asymptotic behaviour for t of the solutions to a one-dimensional model for thermo-visco-plastic behaviour is investigated in this paper. The model consists of a coupled system of nonlinear partial differential equations, representing the equation of motion, the balance of the internal energy, and a phase evolution equation, determining the evolution of a phase variable. The phase evolution equation can be used to deal with relaxation processes. Rate-independent hysteresis effects in the strain-stress...

Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability

Josef Kalas, Josef Rebenda (2011)

Mathematica Bohemica

We present several results dealing with the asymptotic behaviour of a real two-dimensional system x ' ( t ) = 𝖠 ( t ) x ( t ) + k = 1 m 𝖡 k ( t ) x ( θ k ( t ) ) + h ( t , x ( t ) , x ( θ 1 ( t ) ) , , x ( θ m ( t ) ) ) with bounded nonconstant delays t - θ k ( t ) 0 satisfying lim t θ k ( t ) = , under the assumption of instability. Here 𝖠 , 𝖡 k and h are supposed to be matrix functions and a vector function, respectively. The conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one equation with...

Asymptotic behaviour of nonoscillatory solutions of the fourth order differential equations

Monika Sobalová (2002)

Archivum Mathematicum

In the paper the fourth order nonlinear differential equation y ( 4 ) + ( q ( t ) y ' ) ' + r ( t ) f ( y ) = 0 , where q C 1 ( [ 0 , ) ) , r C 0 ( [ 0 , ) ) , f C 0 ( R ) , r 0 and f ( x ) x > 0 for x 0 is considered. We investigate the asymptotic behaviour of nonoscillatory solutions and give sufficient conditions under which all nonoscillatory solutions either are unbounded or tend to zero for t .

Asymptotic behaviour of oscillatory solutions of n -th order differential equations with quasiderivatives

Miroslav Bartušek (1997)

Czechoslovak Mathematical Journal

Sufficient conditions are given under which the sequence of the absolute values of all local extremes of y [ i ] , i { 0 , 1 , , n - 2 } of solutions of a differential equation with quasiderivatives y [ n ] = f ( t , y [ 0 ] , , y [ n - 1 ] ) is increasing and tends to . The existence of proper, oscillatory and unbounded solutions is proved.

Asymptotic behaviour of solutions of real two-dimensional differential system with nonconstant delay

Josef Rebenda (2009)

Archivum Mathematicum

In this article, stability and asymptotic properties of solutions of a real two-dimensional system x ' ( t ) = 𝐀 ( t ) x ( t ) + 𝐁 ( t ) x ( τ ( t ) ) + 𝐡 ( t , x ( t ) , x ( τ ( t ) ) ) are studied, where 𝐀 , 𝐁 are matrix functions, 𝐡 is a vector function and τ ( t ) t is a nonconstant delay which is absolutely continuous and satisfies lim t τ ( t ) = . Generalization of results on stability of a two-dimensional differential system with one constant delay is obtained using the methods of complexification and Lyapunov-Krasovskii functional and some new corollaries and examples are presented.

Asymptotic behaviour of solutions of some linear delay differential equations

Jan Čermák (2000)

Mathematica Bohemica

In this paper we investigate the asymptotic properties of all solutions of the delay differential equation y’(x)=a(x)y((x))+b(x)y(x),      xI=[x0,). We set up conditions under which every solution of this equation can be represented in terms of a solution of the differential equation z’(x)=b(x)z(x),      xI and a solution of the functional equation |a(x)|((x))=|b(x)|(x),      xI.

Currently displaying 1061 – 1080 of 1233