To the solution of the Solonnikov-Fasano problem with boundary moving on arbitrary law x = γ(t)
Шекарасы x = γ(t) заңдылығымен қозғалатын Солонников-Фазан есебiнiң шешiмi туралы
К решению задачи Солонникова-Фазано при движении границы по произвольному закону x = γ(t)
Jenaliyev M.T. Ramazanov M.I. Tanin A.O.
2021E.A.Buketov Karaganda State University Publish House
Bulletin of the Karaganda University. Mathematics Series
2021#101Issue 137 - 49 pp.
In this paper we study the solvability of the boundary value problem for the heat equation in a domain that degenerates into a point at the initial moment of time. In this case, the boundary changing with time moves according to an arbitrary law x = γ(t). Using the generalized heat potentials, the problem under study is reduced to a pseudo-Volterra integral equation such that the norm of the integral operator is equal to one and it is shown that the corresponding homogeneous integral equation has a nonzero solution.
degenerating domain , heat equation , moving boundary , pseudo-Volterra integral equation
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Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
Buketov Karaganda University, Karaganda, Kazakhstan
Institute of Mathematics and Mathematical Modeling
Buketov Karaganda University
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