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Continuous dependence on data for linear evolution PDEs on the quarter-plane
Andreas Chatziafratis, Spyridon Kamvissis
In this note, we announce a systematic analysis of continuous dependence on the data in classical spaces for the initial-boundary-value problem of the diffusion equation on the hal…
Density in the half-line Schwartz space of functions whose Fourier-Laplace transform has natural boundary the real line
Andreas Chatziafratis, Telemachos Hatziafratis
In this note, we prove that the Fourier-Laplace transform of the typical function (i.e., generic in the sense of Baire category theorem) in the Schwartz class of the half-line, bei…
A note on uniqueness for linear evolution PDEs posed on the quarter-plane
Andreas Chatziafratis, Spyridon Kamvissis
In this paper, we announce a rigorous approach to establishing uniqueness results, under certain conditions, for initial-boundary-value problems for a class of linear evolution par…
Boundary behaviour of the solution of the heat equation on the half line via the Fokas unified transform method
Andreas Chatziafratis
We consider the Fokas method expression for the solution of the heat equation on the half line with Dirichlet data and we study in detail its boundary behaviour near the spatiotemp…