Stability for the Mixed Problem Involving the Wave Equation, with Localized Damping, in Unbounded Domains with Finite Measure

2018 ◽  
Vol 56 (4) ◽  
pp. 2802-2834 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Flávio R. Dias Silva ◽  
Valéria N. Domingos Cavalcanti ◽  
André Vicente
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Unbounded Domains ◽  
Finite Measure ◽  
Localized Damping

Uniform Decay Rates for the Wave Equation with Nonlinear Damping Locally Distributed in Unbounded Domains with Finite Measure

2014 ◽  
Vol 52 (1) ◽  
pp. 545-580 ◽  
Author(s):  
Marcelo M. Cavalcanti ◽  
Flávio R. Dias Silva ◽  
Valéria N. Domingos Cavalcanti
Keyword(s):  
Wave Equation ◽  
Unbounded Domains ◽  
Finite Measure ◽  
Nonlinear Damping ◽  
Decay Rates ◽  
Uniform Decay

Classical and generalized of a mixed problem– solutions for a non-homogeneous wave equation

2019 ◽  
Vol 484 (1) ◽  
pp. 18-20
Author(s):  
A. P. Khromov ◽  
V. V. Kornev
Keyword(s):  
Wave Equation ◽  
Fourier Series ◽  
Mixed Problem ◽  
Homogeneous Equation ◽  
Generalized Solution ◽  
Problem Solution ◽  
Homogeneous Wave ◽  
Homogeneous Wave Equation ◽  
Explicit Expressions

This study follows A.N. Krylov’s recommendations on accelerating the convergence of the Fourier series, to obtain explicit expressions of the classical mixed problem–solution for a non-homogeneous equation and explicit expressions of the generalized solution in the case of arbitrary summable functions q(x), ϕ(x), y(x), f(x, t).

scholarly journals Сlassical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

2020 ◽  
Vol 64 (6) ◽  
pp. 657-662
Author(s):  
V. I. Korzyuk ◽  
J. V. Rudzko
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Mixed Problem ◽  
Method Of Characteristics ◽  
Smooth Boundary ◽  
Analytical Form ◽  
Initial Condition ◽  
One Dimensional ◽  
The One ◽  
Dimensional Wave

In this article, we study the classical solution of the mixed problem in a quarter of a plane and a half-plane for a one-dimensional wave equation. On the bottom of the boundary, Cauchy conditions are specified, and the second of them has a discontinuity of the first kind at one point. Smooth boundary condition is set at the side boundary. The solution is built using the method of characteristics in an explicit analytical form. Uniqueness is proved and conditions are established under which a piecewise-smooth solution exists. The problem with linking conditions is considered.

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