Stability analysis for linear heat conduction with memory kernels described by Gamma functions

Corrado Mascia

doi:10.3934/dcds.2015.35.3569

Article Contents

2015, Volume 35, Issue 8: 3569-3584. Doi: 10.3934/dcds.2015.35.3569

This issue Previous Article Non-localized standing waves of the hyperbolic cubic nonlinear Schrödinger equation Next Article On the blow-up results for a class of strongly perturbed semilinear heat equations

Stability analysis for linear heat conduction with memory kernels described by Gamma functions

Corrado Mascia^1,

1.
Dipartimento di Matematica “G. Castelnuovo”, Università di Roma “La Sapienza”, Piazzale A. Moro, 2, I–00185 Roma

Received: October 2014

Revised: November 2014

Published: May 2017

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Abstract

This paper analyzes heat equation with memory in the case of kernels that are linear combinations of Gamma distributions. In this case, it is possible to rewrite the non-local equation as a local system of partial differential equations of hyperbolic type. Stability is studied in details by analyzing the corresponding dispersion relation, providing sufficient stability condition for the general case and sharp instability thresholds in the case of linear combinations of the first three Gamma functions.

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Mathematics Subject Classification: Primary: 74D05; Secondary: 35L45, 35B35, 76R50.

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