Abstract
In this paper, we consider a heat equation with mixed boundary conditions in a two-dimensional domain with a reentrant corner. This allows the solution to exhibit singularities near the corner as well as at the points where the mixed boundary conditions meet. The aim of this work is to establish a Carleman inequality by constructing a convenient weight function. As a consequence, we prove some control results.
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Sadali, D., Moulay, M.S. A New Carleman Inequality for a Heat Equation in Presence of Singularities and Controllability Consequences. J Dyn Control Syst 27, 51–65 (2021). https://doi.org/10.1007/s10883-020-09476-4
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DOI: https://doi.org/10.1007/s10883-020-09476-4
Keywords
- Mixed boundary conditions
- Semilinear parabolic equations
- Controllability
- Observability
- Carleman inequalities
- Singularities