Jaime E. Muñoz Rivera

Mildly dissipative nonlinear Timoshenko systems : global existence and exponential stability

We consider nonlinear systems of Timoshenko type in a one-dimensional bounded domain. The system has a dissipative mechanism being present only in the equation for the rotation angle; it is a damping effect through heat conduction. The global existence of small, smooth solutions as well as the exponential stability are investigated.

Smoothing properties, decay, and global existence of solutions to nonlinear coupled systems of thermoelastic type

We consider a nonlinear coupled system of evolution equations, the simplest of which models a thermoelastic plate. Smoothing and decay properties of solutions are investigated as well as the local well-posedness and the global existence of solutions. For the system of standard thermoelasticity it is proved that there is no similar smoothing effect.

Asymptotic behavior of the energy for a class of weakly dissipative second-order systems with memory

A class of second-order abstract systems with memory and Dirichlet boundary conditions is investigated. By suitable Liapunov functionals, existence of solutions as well as asymptotic behavior, are determined. In particular, when the memory kernel decays exponentially, the polynomially decay of the solutions is proved.

Decay rates of solutions of an anisotropic inhomogeneous

AbstractWe consider the anisotropic and inhomogeneous viscoelastic equation and we prove that the first and second order energy decay polynomially as time goes to infinity when the relaxation function also decays polynomially to zero. That is, if the kernelGijkl satisfies

-dimensional viscoelastic equation with polynomially decaying kernels

\dot G_{ijkl} \leqq - c_0 G_{ijkl}^{1 + \frac{1}{p}} ;and G_{ijkl} ,G_{ijkl}^{1 + \frac{1}{p}} \in L^1 (\mathbb{R})for p > 2such that 2^m - 1< p,

Existence and exponential decay in nonlinear thermoelasticity

then the first and second order energy decay as

Multidimensional contact problems in thermoelasticity

\frac{1}{{(1 + t)^q }}