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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.

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