Abstract
In spaces of classical functions with power weight, we prove the correct solvability of a boundary-value problem for parabolic equations with an arbitrary power order of degeneracy of coefficients with respect to both time and space variables.
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REFERENCES
L. D. Landau and E. M. Lifshits, Quantum Mechanics [in Russian], Fizmatgiz, Moscow (1963).
I. D. Pukal's'kyi, “One-sided nonlocal boundary-value problem for singular parabolic equations,” Ukr. Mat. Zh., 53, No.11, 1521–1531 (2001).
I. D. Pukal'skii, “Problem with oblique derivative for a nonuniformly parabolic equation,” Differents. Uravn., 37, No.12, 1521–1531 (2001).
S. D. Eidel'man, Parabolic Systems [in Russian], Nauka, Moscow (1964).
M. I. Matiichuk, Parabolic Singular Boundary-Value Problems [in Ukrainian], Institute of Mathematic, Ukrainian Academy of Sciences, Kyiv (1999).
L. I. Kamyshin and V. N. Maslennikova, “Boundary estimates of Schauder type for a solution of a problem with oblique derivative for a parabolic equation in a noncylindrical domain,” Sib. Mat. Zh., 7, No.1, 83–128 (1966).
S. Agmon, A. Douglis, and L. Nirenberg, Estimates near the Boundary for Solutions of Elliptic Equations [Russian translation], Inostrannaya Literatura, Moscow (1962).
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 377–387, March, 2005.
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Pukal'skii, I.D. Boundary-Value Problem for Linear Parabolic Equations with Degeneracies. Ukr Math J 57, 453–465 (2005). https://doi.org/10.1007/s11253-005-0202-y
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DOI: https://doi.org/10.1007/s11253-005-0202-y