Violation of the maximum principle and negative solutions for pulse propagation in Guyer-Krumhansl model

Heat transport in Guyer-Krumhansl model is studied and analytical solutions for the proper one-dimensional differential equation are explored by the operational method. Exact analytical solution is demonstrated. With its help sudden heat surge propagation is analytically described and compared with the solution for gradual heat wave propagation. The example of the application of the study to the heat transport in ultra-thin films is given. Influence of the Knudsen number on heat transport for short pulses and for gradual heat waves is demonstrated. The negativity and the maximum principle violation for the obtained solutions are discussed.