scholarly journals The Exact Bounded Solution to an Initial Boundary Value Problem for 1D Hyperbolic Equation with Interior Degeneracy. I. Separation of Variables

2020 ◽  
Vol 28 (2) ◽  
pp. 2
Author(s):  
Vladimir L. Borsch ◽  
Peter I. Kogut
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Bounded Solution ◽  
Separation Of Variables ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Initial Boundary Value ◽  
Interior Degeneracy

scholarly journals On the connection between solutions of initial boundary-value problems for a some class of integro-differential PDE and a linear hyperbolic equation

2019 ◽  
Vol 21 (4) ◽  
pp. 413-429
Author(s):  
Pavel N. Burago ◽  
Albert I. Egamov
Keyword(s):  
Integral Operator ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Fourier Method ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Phase Constraint ◽  
Initial Boundary Value

We consider the second initial boundary-value problem for a certain class of second-order integro-differential PDE with integral operator. The connection of its solution with the solution of the standard second linear initial boundary-value problem for the hyperbolic equation is shown. Thus, the nonlinear problem is reduced to a standard linear problem, whose numerical solution can be obtained, for example, by the Fourier method or Galerkin method. The article provides examples of five integro-differential equations for various integral operators as particular representatives of the class of integro-differential equations for a better understanding of the problem. The application of the main theorem to these examples is shown. Some simple natural requirement is imposed on the integral operator; so, in four cases out of five the problem’s solution satisfies some phase constraint. The form of these constraints is of particular interest for the further research.

scholarly journals INITIAL-BOUNDARY VALUE PROBLEM FOR ONE-DIMENSION HYPERBOLIC EQUATION WITH INTEGRAL BOUNDARY CONDITION

2017 ◽  
Vol 17 (8) ◽  
pp. 95-101
Author(s):  
M.V. Strigun
Keyword(s):  
Boundary Value Problem ◽  
Hyperbolic Equation ◽  
Boundary Value ◽  
Integral Condition ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Nonlocal Integral Condition ◽  
Initial Boundary Value

In this paper, we study an initial-boundary value problem with nonlocal integral condition for a hyperbolic equation. The existence and uniqueness of a generalized solution of the problem is proved.

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