Geodesic
Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations
Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1961-1982 Cet article a éte moissonné depuis la source EMS Press

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We consider a class of semi-linear dissipative hyperbolic equations in which the operator associated to the linear part has a nontrivial kernel. Under appropriate assumptions on the nonlinear term, we prove that all solutions decay to 0, as t→∞, at least as fast as a suitable negative power of t. Moreover, we prove that this decay rate is optimal in the sense that there exists a nonempty open set of initial data for which the corresponding solutions decay exactly as that negative power of t.
DOI : 10.4171/jems/635
Classification : 35-XX
Keywords: Semi-linear hyperbolic equation, dissipative hyperbolic equations, slow solutions, decay estimates, energy estimates 
@article{JEMS_2016_18_9_a3,
     author = {Marina Ghisi and Massimo Gobbino and Alain Haraux},
     title = {Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations},
     journal = {Journal of the European Mathematical Society},
     pages = {1961--1982},
     year = {2016},
     volume = {18},
     number = {9},
     doi = {10.4171/jems/635},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/635/}
}
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Marina Ghisi; Massimo Gobbino; Alain Haraux. Optimal decay estimates for the general solution to a class of semi-linear dissipative hyperbolic equations. Journal of the European Mathematical Society, Tome 18 (2016) no. 9, pp. 1961-1982. doi: 10.4171/jems/635

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