Heat conduction: a telegraph-type model with self-similar behavior of solutions
Abstract
For heat flux q and temperature T we introduce a modified Fourier--Cattaneo law qt+ l qt= - kTx . The consequence of it is a non-autonomous telegraph-type equation. % ε Stt + at St = Sxx . This model already has a typical self-similar solution which may be written as product of two travelling waves modulo a time-dependent factor and might play a role of intermediate asymptotics.
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