Geodesic
General decay and well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation with memory
Filomat, Tome 35 (2021) no. 5, p. 1745

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DOI

In this paper, we consider the Cauchy problem of a third order in time nonlinear equation known as the Jordan-Moore-Gibson-Thompson (JMGT) equation with the presence of both memory. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result, and we show a local existence result in appropriate function spaces. Finally, we prove a global existence result for small data, and we prove the uniqueness of the generalized solution.
DOI : 10.2298/FIL2105745B
Classification : 35A07, 35D05, 35G05
Keywords: Jordan-Moore-Gibson-Thompson (JMGT), General decay, Memory term, Relaxation function 
Salah Boulaaras; Abdelbaki Choucha; Djamel Ouchenane. General decay and well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation with memory. Filomat, Tome 35 (2021) no. 5, p. 1745 . doi: 10.2298/FIL2105745B
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     title = {General decay and well-posedness of the {Cauchy} problem for the {Jordan-Moore-Gibson-Thompson} equation with memory},
     journal = {Filomat},
     pages = {1745 },
     year = {2021},
     volume = {35},
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     doi = {10.2298/FIL2105745B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2105745B/}
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