Evolution Equations in Hilbert Spaces via the Lacunae Method

Controllability of Semilinear Stochastic Delay Evolution Equations in Hilbert Spaces

The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given. 1. Introduction. The fixed point technique is widely used as a tool to study the controllability of nonlinear systems in finite-and infinite-dimensi...

Generalized Frames in Hilbert Spaces

Anti-periodic Solutions to Strongly Nonlinear Evolution Equations in Hilbert Spaces

We prove the existence of strong solutions to a nonlinear evolution equation of the form  u′(t) + g(t) = f(t) + h(t) g ∈ SL2{∂φ(u(·))} f ∈ SL2{F (·, u(·))} u(0) = −u(T ), in a Hilbert space H, where φ : D(∂φ) ⊂ H → IR+ is a proper, convex, l.s.c. function of compact type, F : [ 0, T ]×D(∂φ)→ 2 is a multifunction which is demiclosed and dominated in some sense by ∂φ and h ∈ L(0, T ;H) is suf...

Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces

and Applied Analysis 3

Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces

We consider the Cauchy problem for the first and the second order differential equations in Banach and Hilbert spaces with an operator coefficient A(t) depending on the parameter t. We develop discretization methods with high parallelism level and without accuracy saturation; i.e., the accuracy adapts automatically to the smoothness of the solution. For analytical solutions the rate of converge...