Carleman Estimates and Controllability of Linear Stochastic Heat Equations

Journal Article · Wed Mar 12 04:00:00 EST 2003 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-002-0757-Z· OSTI ID:21064237

Barbu, V; Rascanu, A ^[1]

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1. Facultatea de Matematica, Universitatea 'Alexandru Ioan Cuza', 6600 Iasi (Romania)

This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat equation (with Dirichlet boundary conditions in the bounded domain D subset of R{sup d} and multiplicative noise):d{sub t}y{sup u}-{delta}y{sup u}+ay{sup u}dt = f dt+1{sup D{sup 0}}u dt+by d{beta}{sub t} in ]0,T]xD, y{sup u}=0 on ]0,T]x{partial_derivative}D, y{sup u}(0)=y{sub 0} in D, and for the corresponding backward dual equation:d{sub t}p{sup v}+{delta}p{sup v}dt-ap{sup v}dt+bk{sup v}dt 1{sub D{sub 0}}v dt+k{sup v}d{beta}{sub t} in [0,T[xD, p{sup v}=0 on [0,T[x{partial_derivative}D, p{sup v}(T)={eta} in D. We prove the null controllability of the backward equation and obtain partial results for the controllability of the forward equation.

• OSTI ID: 21064237
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 47; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIRICHLET PROBLEM
EQUATIONS
HEAT
NOISE
STOCHASTIC PROCESSES