Abstract: This paper studies the approximate controllability issue of an abstract semilinear stochastic control system with nonlocal conditions. Sufficient conditions are formulated and proved for the approximate controllability of such systems by splitting the given semilinear system into two systems, namely a semilinear deterministic system and a linear stochastic system. To prove the approxi...

A class of optimal control problems of hybrid nature governed by semilinear parabolic equations is considered. These problems involve the optimization of switching times at which the dynamics, the integral cost, and the bounds on the control may change. Firstand secondorder optimality conditions are derived. The analysis is based on a reformulation involving a judiciously chosen transformation ...

The paper is concerned with conservative solutions to the nonlinear wave equation utt−c(u) ( c(u)ux ) x = 0. For an open dense set of C initial data, we prove that the solution is piecewise smooth in the t-x plane, while the gradient ux can blow up along finitely many characteristic curves. The analysis is based on a variable transformation introduced in [7], which reduces the equation to a sem...

Abstract. We discuss a general framework for the numerical solution of a family of semilinear elliptic problems whose leading differential operator is the Laplacian. A problem is first transformed to one on a standard domain via a conformal mapping. The boundary value problem on the standard domain is then reduced to an equivalent integral operator equation. We employ the Galerkin method to sol...

This paper is devoted to establishing local and global existence theorems for autonomous semilinear parabolic initial value problems. The local existence theorems do not require Lipchitz condition on nonlinear term. The global existence theorem is an extension of the well-known result of Fujita-Weissler for semilinear heat equations to general autonomous semilinear parabolic equations and systems.

A semilinear space S is homogeneous if, whenever the semilinear structures induced on two finite subsets S1 and S2 of S are isomorphic, there is at least one automorphism of S mapping S1 onto S2. We give a complete classification of all finite homogeneous semilinear spaces. Our theorem extends a result of Ronse on graphs and a result of Devillers and Doyen

A construction of finite semifield planes of order n using irreducible semilinear transformations on a finite vector space of size n is shown to produce fewer than √ n log2 n different nondesarguesian planes.

have been extensively studied. Various existence and uniqueness results are given in [1], [2], and [3], to name a few. More recently, in [4], it is shown that by certain transformations the boundary layer equations for the class of non-Newtonian uids named pseudoplastic can be generalized in the above form for the ODE case n = 1. Under this physical interpretation the above equation, considered...

In this paper we give a necessary and sufficient conditions for approximate controllability of a wide class of semilinear nonautonomous systems in Hilbert spaces. This is done by employing skew-product semi-flows technique. As an application we prove the approximate controllability of a broad class of nonautonomous semilinear reaction diffusion equations which includes the semilinear heat equat...