Hyperbolic-like estimates for higher order equations

Blow-up Estimates for Higher-order Semilinear Parabolic Equations

A Posteriori Error Estimates for Mixed Finite Element Galerkin Approximations to Second Order Linear Hyperbolic Equations

In this article, a posteriori error analysis for mixed finite element Galerkin approximations of second order linear hyperbolic equations is discussed. Based on mixed elliptic reconstructions and an integration tool, which is a variation of Baker’s technique introduced earlier by G. Baker (SIAM J. Numer. Anal., 13 (1976), 564-576) in the context of a priori estimates for a second order wave equ...

On Solvability of Ill Posed Initial–boundary Value Problems for Higher Order Nonlinear 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 > ...

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.