The hyperbolic-parabolic model \(\begin{aligned} \left\{ \begin{array}{ll} u_{tt} = u_{xx} - \big (f(\Theta )\big )_x, \qquad & x\in \Omega , \ t>0, \\ \Theta _t = \Theta _{xx} - f(\Theta ) u_{xt}, \qquad & x\in \Omega , \ t>0, \end{array} \right. \end{aligned}\) for the evolution of the displacement variable u and the temperature \(\Theta \ge 0\) during thermoelastic interaction in a one-dimensional bounded interval \(\Omega \) is considered. Whereas the literature has provided comprehensive results on global solutions for sufficiently regular initial data \((u_0,u_{0t},\Theta _0)=(u,u_t,\Theta )|_{t=0}\) when \(f\equiv id\) , it seems to have remained open so far how far a solution theory can be built solely on the two fundamental physical principles of energy conservation and entropy nondecrease. The present manuscript addresses this by asserting global existence of weak solutions under assumptions which are energy- and entropy-minimal in the sense of allowing for any initial data \(u_0\in W_0^{1,2}(\Omega )\) , \(u_{0t} \in L^2(\Omega )\) and \(0\le \Theta _0\in L^1(\Omega )\) , and which apply to arbitrary \(f\in C^1([0,\infty ))\) with \(f(0)=0\) and \(f'>0\) on \([0,\infty )\) .
