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Asymptotic behavior of solutions of neutral nonlinear differential equations

Jozef Džurina (2002)

Archivum Mathematicum

In this paper we study asymptotic behavior of solutions of second order neutral functional differential equation of the form x ( t ) + p x ( t - τ ) ' ' + f ( t , x ( t ) ) = 0 . We present conditions under which all nonoscillatory solutions are asymptotic to a t + b as t → ∞ , with a , b ∈ R . The obtained results extend those that are known for equation u ' ' + f ( t , u ) = 0 .

Asymptotic behavior of solutions of third order delay differential equations

Mariella Cecchi, Zuzana Došlá (1997)

Archivum Mathematicum

We give an equivalence criterion on property A and property B for delay third order linear differential equations. We also give comparison results on properties A and B between linear and nonlinear equations, whereby we only suppose that nonlinearity has superlinear growth near infinity.

Asymptotic behavior of solutions to an area-preserving motion by crystalline curvature

Shigetoshi Yazaki (2007)

Kybernetika

Asymptotic behavior of solutions of an area-preserving crystalline curvature flow equation is investigated. In this equation, the area enclosed by the solution polygon is preserved, while its total interfacial crystalline energy keeps on decreasing. In the case where the initial polygon is essentially admissible and convex, if the maximal existence time is finite, then vanishing edges are essentially admissible edges. This is a contrast to the case where the initial polygon is admissible and convex:...

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...

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