Abstract
For a wave equation with sources, new running-wave type solutions are built. The results are expressed in terms of the heat transfer theory. We study two types of alternating volume energy sources qυ with a nonlinear temperature dependence T. Let qυ(Т = Т1 ) = 0 where Т1 is the temperature of the source sign change. The source is positive at Т>Т1 (heat input) and negative at Т<Т1 (heat output) when is has technical origin. A source of biological origin differs from technical ones. It serves as a compensator: at Т>Т1 it takes the heat in; at Т<Т1 , it gives the heat out. Three types of analytical solutions are obtained: the sole wave, the kink structure, and the wave chain. Subsonic and supersonic wave processes are studied with respect to the rate of heat perturbations. The examples for a non-classical phenomenon of "negative heat capacity" are given when heat input/output leads to a temperature decrease/increase. We have considered a nonlinear medium liable to an exact analytical description of a wave problem with a having a resonance type of the temperature dependence: its oscillations have a crescent amplitude. As an example of physical interpretation for one solution, the rate of crystal growth is calculated as a function of the melt undercooling.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
