The utilization of total mass to determine the switching points in the symmetric boundary control problem with a linear reaction term

    Authors

    J. R. Cannon;M. Salman

    Comments

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    Abbreviated Journal Title

    J. Math. Anal. Appl.

    Keywords

    diffusion problem; nonlocal boundary value problems; control; REACTION-DIFFUSION EQUATIONS; NONLOCAL BOUNDARY; Mathematics, Applied; Mathematics

    Abstract

    The authors study the problem it u(t) = u(xx) - u, 0 < x < 1, t > 0; u (x, 0) = 0, and it (0, t) = u (1, t) = psi(t), where sigma (t) = u(0) for t(2k) < t < t(2k+1) and psi (t) = 0 for t(2k+1) < t < t(2k+2) k = 0, 1, 2, with t(0) = 0 and the sequence tk is determined by the equations integral(0)(1) u (x, t(k)) dx M, for k = 1, 3, 5,..., and integral(0)(1) u(x, t(k)) dx = m, for k = 2, 4, 6,... and where 0 < m < M. Note that the switching points t(k), 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 u(x)(0, t) = u(x) (1, t) = psi(t) is also considered and analyzed. (c) 2005 Published by Elsevier Inc.

    Journal Title

    Journal of Mathematical Analysis and Applications

    Volume

    311

    Issue/Number

    1

    Publication Date

    1-1-2005

    Document Type

    Article

    Language

    English

    First Page

    147

    Last Page

    161

    WOS Identifier

    WOS:000232236100012

    ISSN

    0022-247X

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