The utilization of total mass to determine the switching points in the symmetric boundary control problem with a linear reaction term |
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Authors: | J.R. Cannon |
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Affiliation: | Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA |
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Abstract: | The authors study the problem , and u(0,t)=u(1,t)=ψ(t), where ψ(t)=u0 for t2k<t<t2k+1 and ψ(t)=0 for , with t0=0 and the sequence tk is determined by the equations , for , and , for k=2,4,6,… and where 0<m<M. Note that the switching points , 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. |
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Keywords: | Diffusion problem Nonlocal boundary value problems Control |
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