Es werden lineare und nichtlineare Evolutionsgleichungen vom thermoelastischen Typ untersucht hinsichtlich der Existenz von Lösungen und der Asymptotik der Lösungen für große Zeiten.
We investigate linear and nonlinear evolution equations of thermoelastic type with respect to the existence of solutions and their asymptotic behavior for large times
- FB Mathematik und Statistik
|(2002): Global stability for damped Timoshenko systems|
We consider a nonlinear Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. The system has a dissipative mechanism through frictional damping being present only in the equation for the rotation angle. We first give an alternative proof for a sufficient and necessary condition for exponential stability for the linear case. Polynomial stability is proved in general. The global existence of small, smooth solutions and the exponential stability is investigated for the nonlinear case.
|(2002): 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.
|(2001): Thermoelasticity with second sound : exponential stability in linear and nonlinear 1-d|
We consider linear and nonlinear thermoelastic systems in one space dimension where thermal disturbances are modeled propagating as wave-like pulses traveling at finite speed. This removal of the physical paradox of infinite propagation speed in the classical theory of thermoelasticity within Fourier's law is achieved using Cattaneo's law for heat conduction. For different boundary conditions, in particular for those arising in pulsed laser heating of solids, the exponential stability of the now purely, but slightly damped, hyperbolic linear system is proved. A comparison to classical hyperbolic-parabolic thermoelasticity is given. For Dirichlet type boundary conditions - rigidly clamped, constant temperature - the global existence of small, smooth solutions and the exponential stability are proved for a nonlinear system.
|(2001): Asymptotic behavior of solutions in linear 2- or 3-d thermoelasticity with second sound|
We consider thermoelastic systems in two or three space dimensions where thermal disturbances are modeled popagating as wavelike pulses traveling at finite speed. This is done using Cattaneo's law for heat conduction instead of Fourier's law. For Dirichlet type boundary conditions, the exponential stability of the now purely, but slightly damped, hyperbolic system is proved in the radially symmetric case.