Keywords: boundary control, parabolic-hyperbolic system, integral time delays, Neumann problem, quadratic programming method, Hilbert space In this paper, we consider optimal boundary control problems for parabolic-hyperbolic systems in which time delays appear in the integral form in the state equations. The right-hand side of the state equation and the initial and boundary conditions are not ...

Abstract: In this paper, we discuss some new Gronwall-Bellman type delay integral inequalities in two independent variables on time scales, which contain arbitrary nonlinear items on unknown functions outside the integrals as well as inside the integrals. The inequalities established have different forms compared with the existing GronwallBellman type inequalities so far in the literature. As a...

By using the averaging technique, some integral oscillation criteria are obtained for even order damped delay differential equations. 1 – Introduction This paper deals with the oscillatory behavior of the even order damped delay differential equation (1.1) ( Φ(xn−1)(t)) )′ + p(t)Φ(x(n−1)(t)) + f ( t, x[ τ01(t) ], ..., x[ τ0m(t) ], ..., x(n−1)[ τn−11(t) ], ..., x (n−1)[ τn−1m(t) ] ) = 0 for t ≥ ...

In this article, we study the asymptotical stability in p-th moment of mild solutions to a class of fractional impulsive partial neutral stochastic integro-differential equations with state-dependent delay in Hilbert spaces. We assume that the linear part of this equation generates an α-resolvent operator and transform it into an integral equation. Sufficient conditions for the existence and as...

This paper is concerned with the regulation control of a one-dimensional reaction–diffusion equation in presence state-delay reaction term. The objective to achieve PI right Dirichlet trace command selected as left trace. design strategy consists controller on finite dimensional truncated model obtained by spectral reduction. By an adequate selection number modes original infinite-dimensional s...

an ecient method, based on the legendre wavelets, is proposed to solve thesecond kind fredholm and volterra integral equations of hammerstein type.the properties of legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known newton's method. examples assuring eciencyof the method and ...

In this paper we formulate new curvature functions on Sn via integral operators. For certain even orders, these curvature functions are equivalent to the classic curvature functions defined via differential operators, but not for all even orders. Existence result for antipodally symmetric prescribed curvature functions on Sn is obtained. As a corollary, the existence of a conformal metric for a...