Wave equations with time-dependent dissipation II. Effective dissipation
نویسندگان
چکیده
منابع مشابه
Scattering and modified scattering for abstract wave equations with time-dependent dissipation
We consider the initial-value problem of abstract wave equations with weak dissipation. We show that under conditions on the dissipation coefficient and its derivative the solutions to the abstract dissipative equation are closely related to solutions of the free problem multiplied by a decay function. This paper gives the counterpart to a recent paper of T.Yamazaki [Adv. Differential Equ., 11(...
متن کاملL–L decay estimates for wave equations with monotone time-dependent dissipation
This expository article is intended to give an overview about recently achieved results on asymptotic properties of solutions to the Cauchy problem utt −∆u + b(t)ut = 0, u(0, ·) = u1, Dtu(0, ·) = u2 for a wave equation with time-dependent dissipation term. The results are based on structural properties of the Fourier multipliers representing its solution. The article explains the general philos...
متن کاملOn Wave Equations with Boundary Dissipation of Memory Type
The undamped wave equation on an open domain of arbitrary dimension and boundary of class C 1 is considered. On parts of the boundary the normal derivative of the solution equals the convolution of its time derivative with a measure of positive type. This setting subsumes standard disssipative boundary conditions as well as the interaction with vis-coelastic boundary materials. Applying methods...
متن کاملWave Energy Dissipation Using Perforated and Non Perforated Piles
The indispensable vital structure in any harbor is a breakwater in order to make available calm water region inshore. Pile breakwater can be employed as a small coastal protection structure where tranquility required is low. This study is concerned with CFD study on the performance of perforated hollow pile to dissipate wave energy and the novelty of this investigation is the role of perforatio...
متن کاملGeometric dissipation in kinetic equations
A new symplectic variational approach is developed for modeling dissipation in kinetic equations. This approach yields a double bracket structure in phase space which generates kinetic equations representing coadjoint motion under canonical transformations. The Vlasov example admits measure-valued single-particle solutions. Such solutions are reversible; and the total entropy is a Casimir, and ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2007
ISSN: 0022-0396
DOI: 10.1016/j.jde.2006.06.004