2026-04-17T00:50:13Zhttps://recercat.cat/oai/requestoai:recercat.cat:10256/170462025-04-30T23:47:58Zcom_2072_452955com_2072_2054col_2072_453069
RECERCAT
author
Pellicer Sabadí, Marta
author
Said-Houari, B.
info:eu-repo/date/embargoEnd/2020-10-012019-10-01
In this paper, we study the Moore–Gibson–Thompson equation in (Formula presented.), which is a third order in time equation that arises in viscous thermally relaxing fluids and also in viscoelastic materials (then under the name of standard linear viscoelastic model). First, we use some Lyapunov functionals in the Fourier space to show that, under certain assumptions on some parameters in the equation, a norm related to the solution decays with a rate (Formula presented.). Since the decay of the previous norm does not give the decay rate of the solution itself then, in the second part of the paper, we show an explicit representation of the solution in the frequency domain by analyzing the eigenvalues of the Fourier image of the solution and writing the solution accordingly. We use this eigenvalues expansion method to give the decay rate of the solution (and also of its derivatives), which results in (Formula presented.) for (Formula presented.) and (Formula presented.) when (Formula presented.)This work is partially supported by the grants MTM2014-52402-C3-3-P (Spain) and MPC
UdG 2016/047 (U. de Girona, Catalonia). Also, M. Pellicer is part of the Catalan research
group 2014 SGR 1083
Tots els drets reservats info:eu-repo/semantics/openAccess
Fourier, Transformacions de
Fourier transformations
Equacions diferencials parcials
Differential equations, Partial
Matemàtica aplicada
Applied mathematics
Anàlisi numèrica
Numerical analysis
Wellposedness and Decay Rates for the Cauchy Problem of the Moore–Gibson–Thompson Equation Arising in High Intensity Ultrasound
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion peer-reviewed