Decay Rates of the Solutions to the Thermoelastic Bresse System of Types I and III

2017/02/14 by Fernando A. Gallego, F. A. Gallego, Gallego, F. A. +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Elasticity and Wave Propagation #FOS: Mathematics #Stability and Controllability of Differential Equations #Thermoelastic and Magnetoelastic Phenomena #math.AP

paper · pdf · doi:10.48550/arxiv.1702.04198

arxiv created 2017/02/14 · openalex publication_date 2017/02/14 · arxiv updated 2017/02/15 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the energy decay for the thermoelastic Bresse system in the whole line with two different dissipative mechanism, given by heat conduction (Types I and III). We prove that the decay rate of the solutions are very slow. More precisely, we show that the solutions decay with the rate of (1+t)^-(1)/(8) in the L²-norm, whenever the initial data belongs to L¹(R) ∩ H^s(R) for a suitable s. The wave speeds of propagation have influence on the decay rate with respect to the regularity of the initial data. This phenomenon is known as regularity-loss. The main tool used to prove our results is the energy method in the Fourier space.

Citations

• Hyperbolic Thermoelasticity: A Review of Recent Literature

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