Conditions For Hyperbolic Equation Research Articles

PROBLEM WITH TIME-DEPENDENT BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION

In this paper, we consider a problem for hyperbolic equation with standard initial data and nonlocal dynamic conditions. Such conditions may arise when a thick short bar fixed by point forces and springs. The existence and uniqueness of the problem are proved. The proof is mainly based on a priori estimates and Galerkin procedure.

A PROBLEM WITH SECOND KIND INTEGRAL CONDITIONS FOR HYPERBOLIC EQUATION

In this paper, we consider a problem for one-dimensional hyperbolic equation with second kind integral conditions and prove unique solvability. To prove this statement we suggest a new approach. The main idea of it is that given nonlocal integral condition is equivalent with a different condition, nonlocal as well but this new condition enables us to introduce a definition of a generalized solution bazed on an integral identity and derive a priori estimates of a required solution in Sobolev space. This approach shows that integral conditions are closely connected with dynamical conditions.

ON CERTAIN INITIAL-BOUNDARY VALUE PROBLEMS WITH NONLINEAL BOUNDARY CONDITIONS FOR HYPERBOLIC EQUATION

In this paper, we study the solvability of a problem for a nonlinear hyperbolic equation with a nonlinear boundary conditions. The unique solvability is proved.