Certain nonlocal problem for a degenerate hyperbolic equation

1992 ◽  
Vol 51 (3) ◽  
pp. 286-290 ◽  
Author(s):  
L. S. Pul'kina
Keyword(s):  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Degenerate Hyperbolic Equation

scholarly journals ON CERTAIN NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION WITH INTEGRAL CONDITIONS OF THE FIRST KIND

2017 ◽  
Vol 17 (5) ◽  
pp. 29-36
Author(s):  
A.V. Duzheva
Keyword(s):  
Hyperbolic Equation ◽  
Existence And Uniqueness ◽  
Nonlocal Problem ◽  
Integral Condition ◽  
Generalized Solution ◽  
Integral Conditions

In this article, we consider a nonlocal problem for hyperbolic equation with integral conditions of the first kind. The main goal of this article is to show the method which allows to reduce posed problem to the problem with integral condition of the second kind. Existence and uniqueness of generalized solution is proved.

scholarly journals ON SMOOTHNESS OF SOLUTION OF ONE NONLOCAL PROBLEM FOR HYPERBOLIC EQUATION

2021 ◽  
Vol 26 (2) ◽  
pp. 15-22
Author(s):  
V. A. Kirichek
Keyword(s):  
Hyperbolic Equation ◽  
Nonlocal Problem ◽  
Generalized Solution ◽  
Integral Boundary ◽  
Apriori Estimates ◽  
The Space L2 ◽  
Elastic Fixation ◽  
The Right ◽  
Derivatives Of ◽  
Smoothness Of Solution

In this paper we consider a nonlocal problem with integral boundary condition for hyperbolic equation. The conditions of the problem contain derivatives of the first order with respect to both x and t,, which can be interpreted as an elastic fixation of the right end rod in the presence of a certain damper, and since the conditions also contain integral of the desired solution, this condition is nonlocal. It is known that problems with nonlocal integral conditions are non-self-adjoint and, therefore, the study of solvability encounters difficulties that are not characteristic of self-adjoint problems. Additional difficulties arise also due to the fact that one of the conditions is dynamic. The attention of the article is focused on studying thesmoothness of the solution of the nonlocal problem. The concept of a generalized solution is introduced, and the existence of second-order derivatives and their belonging to the space L2 are proved. The proof is basedon apriori estimates obtained in this work.

Sign in / Sign up

Export Citation Format

Share Document