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.
diffusion problem; nonlocal boundary value problems; control; REACTION-DIFFUSION EQUATIONS; NONLOCAL BOUNDARY; Mathematics, Applied; Mathematics
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 of Mathematical Analysis and Applications
"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.