Mixed Problem For Hyperbolic Equation Research Articles

A MIXED PROBLEM FOR THE FOUR-ORDER ONE-DIMENSIONAL HYPERBOLIC EQUATION WITH PERIODIC CONDITIONS

This article considers a classical solution of the boundary problem for the four-order strictly hyperbolic equation with four different characteristics. Note that the well-posed statement of mixed problems for hyperbolic equations not only depends on the number of characteristics, but also on their location. The operator appearing in the equation involves a composition of first-order differential operators. The equation is defined in the half-strip of two independent variables. There are Cauchy’s conditions at the domain bottom and periodic conditions at other boundaries. Using the method of characteristics, the analytic solution of the considered problem is obtained. The uniqueness of the solution is proved. We have also noted that the solution in the whole given domain is a composition of the solutions obtained in some subdomains. Thus, for the obtained classical solution to possess required smoothness, the values of these piecewise solutions, as well as their derivatives up to the fourth order must coincide at the boundary of these subdomains. A classical solution is understood as a function that is defined everywhere at all closure points of a given domain and has all classical derivatives entering the equation and the conditions of the problem.

PERTURBATION RESULTS FOR HYPERBOLIC EVOLUTION SYSTEMS IN HILBERT SPACES

The purpose of this paper is to derive a perturbation theory of evolution systems of the hyperbolic second order hyperbolic equations. We give an example of a partial functional equation as an application of the preceding result in case of the mixed problems for hyperbolic equations of second order with unbounded principal operators.

On the well-posedness of the mixed problem for hyperbolic operators with characteristics of variable multiplicity

The paper is devoted to the study of the well-posedness of mixed problems for hyperbolic equations with constant coefficients and characteristics of variable multiplicity. The authors distinguish a class of higher-order hyperbolic operators with constant coefficients and characteristics of variable multiplicity for which a generalization of the Sakamoto L2-well-posedness of the mixed problem is obtained.

On the regularity of solutions of a mixed problem for hyperbolic equations of second order in a domain with corners

On the regularity of solutions of a mixed problem for hyperbolic equations of second order in a domain with corners

On a characterization of $L^2$-well posed mixed problems for hyperbolic equations of second order

On a characterization of $L^2$-well posed mixed problems for hyperbolic equations of second order

Mixed problems for hyperbolic equations of second order with first order complex boundary operators

Mixed problems for hyperbolic equations of second order with first order complex boundary operators

Fundamental solutions of mixed problems for hyperbolic equations with constant coefficients

Fundamental solutions of mixed problems for hyperbolic equations with constant coefficients

Remarks on $L^2$-well-posed mixed problems for hyperbolic equations of second order

Remarks on $L^2$-well-posed mixed problems for hyperbolic equations of second order

ON EXTERIOR ELLIPTIC PROBLEMS POLYNOMIALLY DEPENDING ON A SPECTRAL PARAMETER, AND THE ASYMPTOTIC BEHAVIOR FOR LARGE TIME OF SOLUTIONS OF NONSTATIONARY PROBLEMS

In this paper elliptic problems in exterior domains polynomially depending on a spectral parameter are considered. These problems are obtained from a mixed problem for hyperbolic equations by substituting for . For such elliptic problems analytic properties of the resolvent are studied in the neighborhood of the point , which permits, for the corresponding nonstationary problem, a complete asymptotic expansion of solutions as .Bibliography: 11 items.

Mixed problem for hyperbolic equation of second order

Mixed problem for hyperbolic equation of second order

On the mixed problem for hyperbolic equations of second order with the Neumann boundary condition

On the mixed problem for hyperbolic equations of second order with the Neumann boundary condition

A Mixed Problem for Hyperbolic Equations of Second Order with a First Order Derivative Boundary Condition

On the mixed problems for hyperbolic equations of second order, only the problems with the Dirichlet condition and with the Neumann condition are studied satisfactorily. Concerning the problems with the other boundary conditions Agmon [1] contains the results on more general boundary conditions in the case when the domain is a half space and the coefficients are constant. And the author showed the not well-posedness in L 2-sense of the problem for the wave equation with an oblique derivative boundary condition [7]. In this paper we extend the results for second order equations of Agmon's paper to the case of variable coefficients and a general domain.

A mixed problem for hyperbolic equations of second order with non-homogeneous Neumann type boundary condition

A mixed problem for hyperbolic equations of second order with non-homogeneous Neumann type boundary condition

On certain mixed problem for hyperbolic equations of higher order, II

On certain mixed problem for hyperbolic equations of higher order, II

On certain mixed problem for hyperbolic equations of higher order

On certain mixed problem for hyperbolic equations of higher order

On certain mixed problem for hyperbolic equations of higher order, III

On certain mixed problem for hyperbolic equations of higher order, III

Mixed problems for hyperbolic equations of second order

Mixed problems for hyperbolic equations of second order

A mixed problem for hyperbolic equations with time-dependent domain

A mixed problem for hyperbolic equations with time-dependent domain