Bounded invertibility and separability of a parabolic type singular operator in the space L2(R2)
Muratbekov M. Muratbekov M. Suleimbekova A.
2021TUBITAK
Turkish Journal of Mathematics
2021#45Issue 52199 - 2210 pp.
In this paper, we consider the operator of parabolic type (Formula presented) ∂u ∂2u Lu= ∂t − ∂x 2 + q (x)u, in the space L2(R2) with a greatly growing coefficient at infinity. The operator is originally defined on C0∞ (R2), where C0∞ (R2) is the set of infinitely differentiable and compactly supported functions. Assume that the coefficient q (x) is a continuous function in R= (−∞, ∞), and it can be a strongly increasing function at infinity. The operator L admits closure in space L 2(R2), and the closure is also denoted by L. In the paper, we proved the bounded invertibility of the operator L in the space L 2(R2) and the existence of the estimate (Formula presented) + ∥q (x)u∥L 2 (R 2) ≤ C (∥Lu∥L 2 (R 2) + ∥u∥L 2 (R 2)), + under certain restrictions on q (x) in addition to the conditions indicated above. Example. q (x) = e100|x|, −∞
Coercive estimate , invertibility , parabolic type operator , separability , singular operator
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Department of Mathematics, Taraz Regional University named after M.Kh. Dulaty, Taraz, Kazakhstan
Center of Information Technologies, Kazakh University of Economics, Finance and International Trade, Nur-Sultan, Kazakhstan
Department of Fundamental Mathematics, L.N. Gumilyov Eurasian National University, Nur-Sultan, Kazakhstan
Department of Mathematics
Center of Information Technologies
Department of Fundamental Mathematics
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