Work

Large-data regular solutions in a one-dimensional thermoviscoelastic evolution problem involving temperature-dependent viscosities

Year: 2025

Type: article

Abstract: The model $$\begin{aligned} \left\{ \begin{array}{l}u_{tt} = \big (\gamma (\Theta ) u_{xt}\big )_x + au_{xx} - \big (f(\Theta )\big )_x, \\[1mm] \Theta _t = \Theta _{xx} + \gamma (\Theta ) u_{xt}^2 - f(\Theta ) u_{xt}, \end{array} \right. \end{aligned}$$ u tt = ( γ ( Θ ) u xt ) x + a u xx - ( f ( Θ ) ) x , [ 1 m m ] Θ t = Θ xx + γ ( Θ ) u xt 2 - f ( Θ ) u xt , for thermoviscoelastic evolution in one-dimensional Kelvin–Voigt materials is considered. By means of an approach based on maximal Sobolev regularity theory of scalar parabolic equations, it is shown that if $$\gamma _0>0$$ γ 0 > 0 is fixed, then there exists $$\delta =\delta (\gamma _0)>0$$ δ = δ ( γ 0 ) > 0

Source: Journal of Evolution Equations

DOI: 10.1007/s00028-025-01144-z

Author: Michael Winkler

Institution: Paderborn University

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: Deutsche Forschungsgemeinschaft, Universität Paderborn