1,721,105 research outputs found
A variational approach to a free boundary problem arising in electro-photography
No full textBarbu, Viorel; Stojanovic, Srdjan. (1991). A variational approach to a free boundary problem arising in electro-photography. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1628
Controlling the free boundary of elliptic variational inequalities on a variable domain
No full textBarbu, Viorel; Stojanovic, Srdjan. (1991). Controlling the free boundary of elliptic variational inequalities on a variable domain. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/1627
Solution of the Bellman equation associated with an infinite-dimensional stochastic control problem and synthesis of optimal control
Full text linkWe prove the existence and uniqueness of the dynamic programming equation for control diffusion processes in Hilbert spaces
Internal Stabilization by Noise of the Navier–Stokes Equation
Full text linkWe show that the Navier-Stokes equation in O C Rd, d = 2, 3, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V (t, ξ) = Σ Ni=1 Vi(t)ψi(ξ) ̇Βi(t), ξ ε O, where {Βi} Ni=1 are independent Brownian motions and {ψi}Ni=1 is a system of functions on O with support in an arbitrary open subset O0 C O. The stochastic control input {Vi}Ni=1 is found in feedback form. The corresponding result for the linearized Navier-Stokes equation was established in [E. Barbu, The internal stabilization by noise of the linearized Navier-Stokes equation, ESAIM Control Optim. Calc. Var., to appear]
Existence of strong solutions for stochastic porous media equation under general monotonicity conditions
Full text linkBarbu V, Da Prato G, Röckner M. Existence of strong solutions for stochastic porous media equation under general monotonicity conditions. Annals of Probability. 2009;37(2):428-452.This paper addresses the existence and uniqueness of strong solutions to stochasic porous media equations dX - Delta Psi(X)dt = B(X)dW(t) in bounded domains of R-d with Dirichlet boundary conditions. Here Psi is a maximal monotone graph in R x R (possibly multivalued) with the domain and range all of R. Compared with the existing literature on stochastic porous media equations, no growth condition on Psi is assumed and the diffusion coefficient Psi might be multivalued and discontinuous. The latter case is encountered in stochastic models for self-organized criticality or phase transition
Kolmogorov equation associated to the stochastic reflection problem on a smooth convex set of a Hilbert space
Full text linkWe consider the stochastic reflection problem associated with a self-adjoint operator A and a cylindrical Wiener process on a convex set K with nonempty interior and regular boundary Σ in a Hilbert space H. We prove the existence and uniqueness of a smooth solution for the corresponding elliptic infinite-dimensional Kolmogorov equation with Neumann boundary condition on Σ
Feedback Optimal Controllers for the Heston Model
Full text linkWe prove the existence of an optimal feedback controller for a stochastic optimization problem constituted by a variation of the Heston model, where a stochastic input process is added in order to minimize a given performance criterion. The stochastic feedback controller is found by solving a nonlinear backward parabolic equation for which one proves the existence and uniqueness of a martingale solution
Erratum to “Uniqueness of the generators of 2D Euler and Stokes flows” [Stochastic Process. Appl. 118 (11) (2008) 2071–2084]
No full textFeedback stabilization of the Cahn-Hilliard type system for phase separation
No full textThis article is concerned with the internal feedback stabilization of the phase field system of Cahn–Hilliard type, modeling the phase separation in a binary mixture. Under suitable assumptions on an arbitrarily fixed stationary solution, we construct via spectral separation arguments a feedback controller having its support in an arbitrary open subset of the space domain, such that the closed loop nonlinear system exponentially reaches the prescribed stationary solution. This feedback controller has a finite dimensional structure in the state space of solutions. In particular, every constant stationary solution is admissible
Existence, uniqueness, and longtime behavior for a nonlinear Volterra integrodifferential equation
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