This paper focuses on the phase transitions of a 2×2 system of mixed type for viscosity-capillarity with periodic initial-boundary condition in a viscoelastic material. By the Liapunov functional method, we prove the existence, uniqueness, regularity and uniform boundedness of the solution. The results are correct even for large initial data.

This paper presents criteria for the existence and uniqueness of solutions to five-point boundary value problems associated with third order differential equations by using matching technique. ’Liapunov-like’ functions are used as a tool to establish existence and uniqueness of solutions by matching two three-point boundary value problems. AMS Mathematics Subject Classification (2000): 34B10, 3...

The existence and comparison theorem of solutions is first established for the quasimonotone delayed reaction-diffusion equations on R by appealing to the theory of abstract functional differential equations. The global asymptotic stability, Liapunov stability and uniqueness of traveling wave solutions are then proved by the elementary superand sub-solution comparison and squeezing methods. Sup...

The essential decorrelation rate of a hyperbolic dynamical system is the decay rate of time-correlations one expects to see stably for typical observables once resonances are projected out. We define and illustrate these notions and study the conjecture that for observables in C1, the essential decorrelation rate is never faster than what is dictated by the smallest unstable Liapunov multiplier.

The Liapunov Razumikhin technique is applied to obtain the uniform asymptotic stability for linear integrodifferential equations in Hilbert spaces, x′(t) = A [ x(t) + ∫ t # F (t− s)x(s)ds ] , t ≥ t0 ≥ 0, (# = 0 or −∞), which occur in viscoelasticity and in heat conduction for materials with memory.

Integral Hamzeh Agahi,1,† Adel Mohammadpour,1,∗ Radko Mesiar,2,3,‡ S. Mansour Vaezpour1,§ Department of Statistics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran 15914, Iran Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Slovak University of Technology, SK-81368 Bratislava, Slovakia Institute of In...

G? = (4 E c* : II d II < PI. I f ~(a) is defined and continuous on [t q, t], we will write xt for the function for which x~(s) = x(t + S) for s E [-q, 01. Hence xt E C, . This paper shows that for a nonlinear one-dimensional differential delay equation a(t) = F;(t, x1(.)) (DDE) one can frequently determine (almost by inspection) if the 0 solution is asymptotically stable and give a region of at...

In the paper we propose a new synchronization principle. To guarantee synchronization between coupled chaotic oscillators, proper coupling constants are selected by the Liapunov stability theory and Hurwitz Theorem. As an example and application, we prove the conjecture [Wu & Chua, 1994] that synchronization between two chaotic Chua’s circuits can be achieved by using the second state as feedba...