Decay rates for Bresse system with arbitrary nonlinear localized damping

In this paper we consider a vibrating system of Bresse type, in a one-dimensional bounded domain with nonlinear localized damping mechanisms acting in all the three wave equations. We obtain some rates of decay for its solutions with no restrictions around the coefficients as well as the condition of equal-speed wave propagation. A new result concerning an internal observability for the conservative system was also proved in order to reach the asymptotics above.     

Energy decay rate of the thermoelastic Bresse system

In this paper, we study the energy decay rate for the thermoelastic Bresse system which describes the motion of a linear planar, shearable thermoelastic beam. If the longitudinal motion and heat transfer are neglected, this model reduces to the well-known thermoelastic Timoshenko beam equations. The system consists of three wave equations and two heat equations coupled in certain pattern. The two wave equations about the longitudinal displacement and shear angle displacement are effectively damped by the dissipation from the two heat equations. Actually, the corresponding energy decays exponentially like the classical one-dimensional thermoelastic system. However, the third wave equation about the vertical displacement is only weakly damped. Thus the decay rate of the energy of the overall system is still unknown. We will show that the exponentially decay rate is preserved when the wave speed of the vertical displacement coincides with the wave speed of longitudinal displacement or of the shear angle displacement. Otherwise, only a polynomial type decay rate can be obtained. These results are proved by verifying the frequency domain conditions.      

Decay rates for delayed abstract thermoelastic systems with Cattaneo law

In this paper we consider a thermoelastic type system with Cattaneo’s law and internal time delay. Under a suitable assumption on the weight of delay, we prove that the exponential stability of this system is reduced to an observability estimate for the corresponding uncontrolled system. The proof of the main results uses the methodology introduced by Haraux (Port Math 46:245–258, 1989) and generalized by Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001). Illustrating example is given.     

Decay estimates for a thermoelastic system in waveguides

We investigate the linear system of thermoelasticity, consisting of an elasticity equation and a heat conduction equation, in a waveguide Ω=(0,1)×Rn−1, with certain boundary conditions. We consider the cases of homogeneous and inhomogeneous systems and prove decay estimates of the solutions, which are a key ingredient to showing the global existence of solutions to non-linear thermoelasticity, after having decomposed the solutions into various parts. We also give a simplified proof to the representation of the solutions to the Cauchy problem of thermoelasticity.     

A General Decay Estimate for a Finite Memory Thermoelastic Bresse System

Applications of Mathematics - This work considers a Bresse system with viscoelastic damping on the vertical displacement and heat conduction effect on the shear angle displacement. A general...     

Stability to weak dissipative Bresse system

In this paper we study the Bresse system with frictional dissipation working only on the angle displacement. Our main result is to prove that this dissipative mechanism is enough to stabilize exponentially the whole system provided the velocities of waves propagations are the same. This result is significative only from the mathematical point of view since in practice the velocities of waves propagations are always different. In that direction we show that when the velocities are not the same, the system is not exponentially stable and we prove that the solution in this case goes to zero polynomially, with rates that can be improved by taking more regular initial data. Finally, we give some numerical result to verify our analytical results.     

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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q相似文献   

A solution of the steady state thermoelastic equations

Résumé Une solution particulière des equations d'équilibrium thermoélastique est derivée d'une fonction potentielle. Cette solution est combinée avec les solutions connues des equations élastostatiques et appliquée à la solution d'une classe particulière de problèmes aux limites.     

Fundamental solution and Cauchy problem for a parabolic system with unbounded coefficients

The purpose of this paper is to obtain a fundamental solution matrix for a second order weakly coupled parabolic system and to solve the associated initial-value problem under a global assumption on the growth at infinity of the coefficients and the initial functions.     

Polynomial approximation to the solution of the Cauchy problem

The Cauchy problem for a nonhomogeneous first-order differential-operator equation of parabolic type in a Hilbert space is considered. Polynomial approximations and estimates of their convergence are obtained which depend on the character of the right-hand side and the initial conditions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 427–429, March, 1991.     

The optimal decay rate for a weak dissipative Bresse system

In this work we consider the Bresse system with frictional damping operating only on the angle displacement and we show that under a certain assertion the solution decays polynomially and the decay rate is optimal.     

Decay solution for the renewal equation with diffusion

In this paper we consider age structured equation with diffusion under nonlocal boundary condition and nonnegative initial data. We prove existence, uniqueness and the positivity of the solution to the above problem. Our main result is to get an exponential decay of the solution for large times toward such a study state. To this end we prove a weighted Poincaré–Wirtinger’s type inequality in unbounded domain.     

Regularization of the solution of the Cauchy problem for the system of Maxwell equations in an unbounded domain

We study the analytic continuation of the solution of the system of Maxwell equations in a spatial unbounded domain from its values on a part of the boundary of this domain. We construct an approximate solution of this problem based on the Carleman matrix method.