Abstract:
We consider the first boundary value problem in a cone with a degeneracy of the domain at the initial moment of time for the heat equation. Own functions for the problem were found. Estimations of the Green’s function are obtained. For the problem with a zero boundary function, we establish unambiguous solvability in a certain class of functions that admits a definite growth when approaching the vertex of a cone. Similar results are obtained for the cone that degenerates at the final point in time. In addition, we consider the first boundary value problem in domains that are degenerate only in terms of variables.
Key words:heat conduction equation, first boundary value problem in a cone, Green’s function, first boundary value problem in time-degenerate domains, first boundary value problem in time-degenerate domains, own functions of the first boundary value problem.
