7 papers
Global solutions and large time stabilization in a model for thermoacoustics in a standard linear solid
Tobias Black, Michael Winkler
This manuscript is concerned with the one-dimensional system \[ \begin{array}{l} Ïu_{ttt} + αu_{tt} = b \big(γ(Î) u_{xt}\big)_x + \big( γ(Î) u_x\big)_x, \\[1mm] Î_t = D Î_{…
Global solvability and stabilization in multi-dimensional small-strain nonlinear thermoviscoelasticity
Michael Winkler
Despite considerable developments in the literature of the past decades, a standing open problem in the analysis of continuum mechanics appears to consist of determining how far th…
A simple model for one-dimensional nonlinear thermoelasticity: Well-posedness in rough-data frameworks
Michael Winkler
In an open bounded interval , the problem \[ u_{tt} = u_{xx} - \big(f(Î)\big)_x, Î_t = Î_{xx} - f(Î) u_{xt}, \] is considered under the boundary conditions $u|_{\partialΩ}…
Large time stabilization of rough-data solutions in one-dimensional nonlinear thermoelasticity
Michael Winkler
In an open bounded real interval , the model for one-dimensional thermoelasticity given by \[ u_{tt} = u_{xx} - \big(f(Î)\big)_x, \qquad Î_t = Î_{xx} - f(Î) u_{xt}, \] is c…
Local strong solutions in a quasilinear Moore-Gibson-Thompson type model for thermoviscoelastic evolution in a standard linear solid
Leander Claes, Michael Winkler
This manuscript is concerned with the evolution system \[ \left\{ \begin{array}{l} u_{ttt} + αu_{tt} = \big(γ(Î) u_{xt}\big)_x + \big( \widehatγ(Î) u_x\big)_x, Î_t = D Î_{xx…
Large-data global solutions to a quasilinear model for viscuos acoustic wave propagation in a non-isothermal setting
Felix Meyer, Michael Winkler
The manuscript considers the model for conversion of mechanical energy into heat during acoustic wave propagation in the presence of temperature-dependent elastic parameters, as gi…