A Nonexistence Result to a Cauchy Problem in Nonlinear One Dimensional Thermoelasticity

Considering the Cauchy problem for a nonlinear system arising in thermoelasticity, it is proved that its solution develops singularities in finite time depending on the size and regularity of the initial data. The present work is distinguished from a previous work by relaxing the requirements on the initial data and allowing for a slightly more general and nonautonomous forcing term besides permitting the insertion of gradient terms in both equations of the system