On trace formulae of the generalised heat potential operator. (English) Zbl 1390.35171
Summary: This paper deals with a generalised heat potential for the degenerate (heat) diffusion equation, which satisfies the initial condition with respect to the time variable. An interesting question having several important applications (in general) is what boundary condition can be put on the generalised heat potential on the lateral boundary of the rectangle so that the degenerate diffusion equation complemented by this boundary condition would have a unique solution in the domain still given by the same formula of the generalised heat potential (with the same kernel). This amounts to finding the trace of the generalised heat potential to the lateral boundary of the rectangle. That is in this work a boundary condition for this potential is found. Obtained boundary conditions in the spatial variable will be nonlocal boundary conditions.
MSC:
| 35K65 | Degenerate parabolic equations |
| 35K70 | Ultraparabolic equations, pseudoparabolic equations, etc. |
Keywords:
trace formula; degenerate diffusion operator; fundamental solution; generalised heat potential operatorReferences:
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