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Scattering and modified scattering for abstract wave equations with time-dependent dissipation. (English) Zbl 1159.35047

Thse authors considered the initial-value problem of abstract wave equations with weak dissipation. Giving some conditions on the dissipation coefficient and it’s derivative, they show that the solutions to the abstract dissipative equation are closely related to the free problem multiplied by a decay function. the result gives the counterpart to the work of T. Yamazaki [Adv. Differ. Equ., 11, No. 4, 419–456 (2006; Zbl 1103.35081)].

MSC:

35L90 Abstract hyperbolic equations
35L15 Initial value problems for second-order hyperbolic equations

Citations:

Zbl 1103.35081
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