Equipartition of energy for higher-order hyperbolic equations

On the Correct Formulation of a Multidimensional Problem for Strictly Hyperbolic Equations of Higher Order

A theorem of the unique solvability of the first boundary value problem in the Sobolev weighted spaces is proved for higherorder strictly hyperbolic systems in the conic domain with special orientation. In the space Rn, n > 2, let us consider a strictly hyperbolic equation of the form p(x, ∂)u(x) = f(x), (1) where ∂ = (∂1, . . . , ∂n), ∂j = ∂/∂xj , p(x, ξ) is a real polynomial of order 2m, m > ...

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear Hyperbolic Equations

The Cauchy Problem for Nonlinear Hyperbolic Equations of Higher order using Modified Decomposition Method

In this paper modified decomposition method is applied to the solvability of nonlinear hyperbolic equations of higher order with initial conditions and illustrated with a few simple examples. The results obtained indicate that Modified Decomposition Method is very effective and simple.

On Some Boundary Value Problems for Nonlinear Degenerate Hyperbolic Equations of Higher Order

The Dirichlet problem and other nonclassical boundary value problems for linear hyperbolic equations with two independent variables have been the subject of various studies (see, e.g., [1]–[8], [10]–[16] and the references therein). However such problems for higher order nonlinear hyperbolic equations still remain unstudied. The present paper is an attempt to fulfill the existing gap. Let m and...

On Lidstone Boundary Value Problem for Higher Order Nonlinear Hyperbolic Equations with Two Independent Variables

Moreover, below it will be assumed that the function f : D×R4mn → R is continuous, the functions φ2i : [0, b] → R, φ2i : [0, b] → R (i = 0, . . . ,m − 1) are 2n–times continuously differentiable, and the functions ψ2k : [0, a] → R, ψ2k : [0, a] → R (i = 0, . . . , n − 1) are continuous. By C2m,2n(D) denote the space of continuous functions u : D → R having the continuous partial derivatives u(j...