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Finite propagation speed for limited flux diffusion equations. (English) Zbl 1142.35455
Summary: We prove that the support of solutions of a limited flux diffusion equation known as a relativistic heat equation evolves at a constant speed, identified as the speed of light \(c\). For that we construct entropy sub- and super-solutions which are fronts evolving at speed \(c\) and prove the corresponding comparison principle between entropy solutions and sub- and super-solutions, respectively. This enables us to prove the existence of discontinuity fronts moving at light’s speed.

MSC:
35K55 Nonlinear parabolic equations
35B40 Asymptotic behavior of solutions to PDEs
80A20 Heat and mass transfer, heat flow (MSC2010)
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