#### Title

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

#### 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

#### ISSN

0022-247X

#### Recommended Citation

"The utilization of total mass to determine the switching points in the symmetric boundary control problem with a linear reaction term" (2005). *Faculty Bibliography 2000s*. 5035.

https://stars.library.ucf.edu/facultybib2000/5035

## Comments

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