Stability of equilibrium solution to inhomogeneous heat equation under a 3-point boundary condition |
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Authors: | Bruce D. Calvert |
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Affiliation: | 1. Department of Mathematics , University of Auckland , Private Bag 92019, Auckland, New Zealand calvert@math.auckland.ac.nz |
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Abstract: | We consider a one-dimensional heat equation with inhomogeneous term, satisfying three-point boundary conditions, such that the temperature at the end is controlled by a sensor at the point η. We show that the integral solution, in the space of continuous functions satisfying the boundary values, converges to the equilibrium solution. This answers a question posed for nonlinear Laplacians, but in the linear case only. |
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Keywords: | three-point boundary value problems heat equation asymptotic stability |
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