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We consider the Fokas method expression for the solution of the heat equationon the half line with Dirichlet data and we study in detail its boundarybehaviour near the spatiotemporal domain boundaries, i.e., the semi-axes,infinity and the origin, by analyzing the integrals involved. We also study theboundary behaviour of the derivatives of the solution. In particular we giveconditions on the data which guarantee the extension of the solution to asmooth function up to the semi-infinite boundaries.

Boundary behaviour of the solution of the heat equation on the half line via the Fokas unified transform method