Title

The Utilization Of Total Mass To Determine The Switching Points In The Symmetric Boundary Control Problem With A Linear Reaction Term

Keywords

Control; Diffusion problem; Nonlocal boundary value problems

Abstract

The authors study the problem ut = uxx - u, 0 < x < 1, t > 0; u (x, 0) = 0, and u(0, t) = u(1, t) = ψ (t), where ψ(t) = u0 for t2k < t < t2k+1 and ψ(t) = 0 for t2k+1 < t < t2k+2, k = 0, 1, 2, with t0 = 0 and the sequence tk is determined by the equations ∫01 u(x, tk) dx = M, for k = 1, 3, 5,..., and ∫01 u(x, tk) dx = m, for k = 2, 4, 6,... and where 0 < m < M. Note that the switching points tk, k = 1, 2, 3,..., are unknown. Existence and uniqueness are demonstrated. Theoretical estimates of the tk and tk+1 - tk are obtained and numerical verifications of the estimates are presented. The case of ux (0, t) = ux (1, t) = ψ(t) is also considered and analyzed. © 2005 Published by Elsevier Inc.

Publication Date

11-1-2005

Publication Title

Journal of Mathematical Analysis and Applications

Volume

311

Issue

1

Number of Pages

147-161

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jmaa.2005.02.030

Socpus ID

24744450788 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/24744450788

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