Initial boundary value problems of fourth order hyperbolic equations

Initial Boundary Value Problems for Hyperbolic Partial Differential Equations

1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0,...

Existence of positive solutions for fourth-order boundary value problems with three- point boundary conditions

In this work, by employing the Krasnosel'skii fixed point theorem, we study the existence of positive solutions of a three-point boundary value problem for the following fourth-order differential equation begin{eqnarray*} left { begin{array}{ll} u^{(4)}(t) -f(t,u(t),u^{prime prime }(t))=0 hspace{1cm} 0 leq t leq 1, & u(0) = u(1)=0, hspace{1cm} alpha u^{prime prime }(0) - beta u^{prime prime pri...

Initial value problems for second order hybrid fuzzy differential equations

Usage of fuzzy differential equations (FDEs) is a natural way to model dynamical systems under possibilistic uncertainty. We consider second order hybrid fuzzy differentia

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

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...