Estimates of the rate of decay of solutions to the impedance mixed problem for the wave equation in a region with noncompact boundary

1999 ◽  
Vol 66 (3) ◽  
pp. 316-322
Author(s):  
L. A. Muravei ◽  
A. V. Filinovskii
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Noncompact Boundary ◽  
Decay Of Solutions ◽  
Rate Of Decay

scholarly journals Exponential decay of solutions of a semilinear Lipschitz Perturbation of Kirchhoff-Carrier Wave Equation

1993 ◽  
Vol 15 (15) ◽  
pp. 17
Author(s):  
Eleni Bisognin
Keyword(s):  
Wave Equation ◽  
Mixed Problem ◽  
Exponential Decay ◽  
Lipschitz Function ◽  
Global Solutions ◽  
Work Study ◽  
Carrier Wave ◽  
Decay Of Solutions ◽  
Lipschitz Perturbation

In this work study the existence of global solutions and exponential decay of energy of the mixed problem for perturbed Kirchhoff-Carrier wave equationu" - M(a(u)) Δu + F(u) + γ u’ = fwhere F is a Lipschitz function.

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).

Decay of solutions of the wave equation outside nontrapping obstacles

1977 ◽  
Vol 30 (4) ◽  
pp. 447-508 ◽  
Author(s):  
Cathleen S. Morawetz ◽  
James V. Ralston ◽  
Walter A. Strauss
Keyword(s):  
Wave Equation ◽  
Decay Of Solutions

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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