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 CMFD, 2016, Volume 62, Pages 140–151 (Mi cmfd314)

Coercive solvability of nonlocal boundary-value problems for parabolic equations

L. E. Rossovskii, A. R. Khanalyev

Department of Applied Math., RUDN University, 6 Miklukho-Maklaya st., 117198 Moscow, Russia

Abstract: In a Banach space $E$ we consider nonlocal problem
for abstract parabolic equation with linear unbounded strongly positive operator $A(t)$ with independent of $t$, everywhere dense in $E$ domain $D=D(A(t))$. This operator generates analytic semigroup $\exp\{-sA(t)\}$ ($s\geq0$).
We prove the coercive solvability of the problem in the Banach space $C_0^{\alpha,\alpha}([0,1],E)$ $(0<\alpha<1)$ with the weight $(t+\tau)^\alpha$. This result was previously known only for a constant operator. We consider applications in the class of parabolic functional differential equations with transformation of spatial variables and in the class of parabolic equations with nonlocal conditions on the boundary of domain. Thus, this describes parabolic equations with nonlocal conditions both in time and in spatial variables.

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UDC: 517.95+517.98

Citation: L. E. Rossovskii, A. R. Khanalyev, “Coercive solvability of nonlocal boundary-value problems for parabolic equations”, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), CMFD, 62, PFUR, M., 2016, 140–151

Citation in format AMSBIB
\Bibitem{RosHan16} \by L.~E.~Rossovskii, A.~R.~Khanalyev \paper Coercive solvability of nonlocal boundary-value problems for parabolic equations \inbook Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A.~L.~Skubachevskii (Peoples' Friendship University of Russia) \serial CMFD \yr 2016 \vol 62 \pages 140--151 \publ PFUR \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd314}