Geodesic
Well-posedness and decay of solutions for a transmission problem with history and delay
Electronic journal of differential equations, Tome 2016 (2016)
In this article, we consider a transmission problem in the presence of history and delay terms. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight of the delay, we prove well-posedness by using the semigroup theory. Also we establish a decay result by introducing a suitable Lyaponov functional.
Classification : 35B37, 35L55, 74D05, 93D15, 93D20
Keywords: wave equation, transmission problem, past history, delay term 
@article{EJDE_2016__2016__a59,
     author = {Li,  Gang and Wang,  Danhua and Zhu,  Biqing},
     title = {Well-posedness and decay of solutions for a transmission problem with history and delay},
     journal = {Electronic journal of differential equations},
     year = {2016},
     volume = {2016},
     zbl = {1331.35223},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a59/}
}
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%A Wang,  Danhua
%A Zhu,  Biqing
%T Well-posedness and decay of solutions for a transmission problem with history and delay
%J Electronic journal of differential equations
%D 2016
%V 2016
%U http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a59/
%G en
%F EJDE_2016__2016__a59
Li,  Gang; Wang,  Danhua; Zhu,  Biqing. Well-posedness and decay of solutions for a transmission problem with history and delay. Electronic journal of differential equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a59/