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 Zap. Nauchn. Sem. POMI, 2018, Volume 477, Pages 35–53 (Mi znsl6736)

Solution of the Cauchy problem for a parabolic equation with singular coefficients

G. I. Bizhanova

Institute of Mathematics and Mathematical Modeling, Ministry of Education and Science, Republic of Kazakhstan, Almaty, Kazakhstan

Abstract: The paper is concerned with the Cauchy problem for the second order parabolic equation with the singular coefficients with respect to $t$ at the first order spatial derivatives. The solution of the problem is constructed in the explicit form. For it, it is defined a weighted Hölder space with the weight as a positive power of $t$. The existence, uniqueness, estimates of the solution are proved.

Key words and phrases: parabolic equations with the singular coefficients, Cauchy problem, weighted Hölder space, existence, uniqueness, estimates of the solution.

 Funding Agency Grant Number Ministry of Education and Science of the Republic of Kazakhstan AP05133898 An article was supported by the grant No. AP05133898 of the Committee of Science of the Ministry of the Education and Science of the Republic of Kazakhstan.

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UDC: 517.95
MSC: 35K15 35K67 35A01 35A02 35A20 35B65

Citation: G. I. Bizhanova, “Solution of the Cauchy problem for a parabolic equation with singular coefficients”, Boundary-value problems of mathematical physics and related problems of function theory. Part 47, Zap. Nauchn. Sem. POMI, 477, POMI, St. Petersburg, 2018, 35–53

Citation in format AMSBIB
\Bibitem{Biz18} \by G.~I.~Bizhanova \paper Solution of the Cauchy problem for a parabolic equation with singular coefficients \inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~47 \serial Zap. Nauchn. Sem. POMI \yr 2018 \vol 477 \pages 35--53 \publ POMI \publaddr St.~Petersburg \mathnet{http://mi.mathnet.ru/znsl6736} 

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