9 papers
Global smooth behavior in Kuznetsov and Westervelt type viscous wave equations: A unifying approach covering -small initial data
Tahir Boudjeriou, Michael Winkler
In a smoothly bounded domain $\Om\subset\R^n$ with and , we consider an initial-boundary value problem for the general viscous wave equation \bas h(u,u_t) u_{tt} = \…
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} τu_{ttt} + αu_{tt} = b \big(γ(Θ) u_{xt}\big)_x + \big( γ(Θ) u_x\big)_x, \\[1mm] Θ_t = D Θ_{xx} + bγ…
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 \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is considered under the boundary conditions $u|_{\partialΩ}=Θ_x|_…
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 \[ u_{tt} = u_{xx} - \big(f(Θ)\big)_x, \qquad Θ_t = Θ_{xx} - f(Θ) u_{xt}, \] is consid…
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(Θ) u_{xt}\big)_x + \big( \widehatγ(Θ) u_x\big)_x, Θ_t = D Θ_{xx} + Γ(Θ…
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…
Describing smooth small-data solutions to a quasilinear hyperbolic-parabolic system by energy analysis
Leander Claes, Michael Winkler
In bounded -dimensonal domains with , this manuscript examines an initial-boundary value problem for the system \[ \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (γ(Θ) \…
blow-up in the Jordan-Moore-Gibson-Thompson equation
Vanja Nikolić, Michael Winkler
The Jordan-Moore-Gibson-Thompson equation \[ τu_{ttt} + αu_{tt} = βΔu_t + γΔu + (f(u))_{tt} \] is considered in a smoothly bounded domain with , whe…