On the Solvability of the Dirichlet Problem for the Heat Equation in a Degenerating Domain
Ramazanov M.I. Kosmakova M.T. Tuleutaeva Z.M.
December 2021Pleiades journals
Lobachevskii Journal of Mathematics
2021#42Issue 153715 - 3725 pp.
Abstract: A domain, degenerating at the initial moment of time, isconsidered. A boundary value problem of heat conduction in thisdomain is studied. By virtue of the isotropy property, thesolvability theorems for given boundary value problem areestablished in weight spaces of essentially bounded functions. Theproof of the theorems is based on the solvability conditions of anonhomogeneous integral equation of the third kind. Using theFourier series method, the problem splits into families ofboundary value problems. The method of representation of thesolution to the boundary value problem in the form of sum ofconstructed thermal potentials is used. The given problem isreduced to the problems of solvability of integral equations. Inaddition, the solvability theorems for the boundary value problemsare proved also for the case, when the axial symmetry property isabsent.
degenerating domain , Fourier method , Green’s function , heat equation , Laplace transform
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Buketov Karaganda University, Karaganda, 470074, Kazakhstan
Karaganda Technical University, Karaganda, 470075, Kazakhstan
Buketov Karaganda University
Karaganda Technical University
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