For a second-order parabolic equation there was established the theory of classical solvability of the Cauchy problem in terms of continuity moduli of problem data. Also there were found some necessary and sufficient conditions for classical solvability of the above mentioned problem without using the idea of continuity modulus.
Biography
Graduated from the Faculty of Mechanics and Mathematics of Novosibirsk State University in 1996. Ph.D. thesis was defended in 1999. A list of my works contains more than 40 titles.
Winner of the All-Russian Contest "Outstanding Young Researchers 2000".
Main publications:
Akhmetov D. R. Ob izomorfizme, porozhdaemom uravneniem teploprovodnosti // Sib. matem. zhurn., 1998, 39(2), 243–260.
Akhmetov D. R. O neobkhodimykh i dostatochnykh usloviyakh klassicheskoi razreshimosti zadachi Koshi dlya lineinykh parabolicheskikh uravnenii // Matem. trudy, 1998, 1(1), 3–28.
Akhmetov D. R. Ob izomorfizme, porozhdaemom lineinym parabolicheskim uravneniem // Sib. matem. zhurn., 1999, 40(3), 493–511.
Akhmetov D. R. Kriterii suschestvovaniya $L_1$-norm u starshikh proizvodnykh reshenii odnorodnogo parabolicheskogo uravneniya // Sib. matem. zhurn., 2000, 41(3), 498–512.
Akhmetov D. R. Ob ubyvanii klassicheskikh reshenii parabolicheskikh uravnenii // Dinamika sploshnoi sredy: Sb. nauch. trudov, SO RAN, 2001, 118, 3–10.
M. M. Lavrent'ev (Jn.), R. Spigler, D. R. Akhmetov, “Regularizing a nonlinear integroparabolic Fokker–Planck equation with space-periodic solutions: existence of strong solutions”, Sibirsk. Mat. Zh., 42:4 (2001), 825–848; Siberian Math. J., 42:4 (2001), 693–714
M. M. Lavrent'ev (Jn.), R. Spigler, D. R. Akhmetov, “Nonlinear integroparabolic equations on unbounded domains: existence of classical solutions with special properties”, Sibirsk. Mat. Zh., 42:3 (2001), 585–609; Siberian Math. J., 42:3 (2001), 495–516
D. R. Akhmetov, “A criterion for the existence of $L_1$-norms for higher-order derivatives of solutions of a homogeneous parabolic equation”, Sibirsk. Mat. Zh., 41:3 (2000), 498–512; Siberian Math. J., 41:3 (2000), 405–418
D. R. Akhmetov, “On an isomorphism generated by a linear parabolic equation”, Sibirsk. Mat. Zh., 40:3 (1999), 493–511; Siberian Math. J., 40:3 (1999), 419–434
D. R. Akhmetov, “On Necessary and Sufficient Conditions for Classical Solvability of the Cauchy Problem for Linear Parabolic Equations”, Mat. Tr., 1:1 (1998), 3–28; Siberian Adv. Math., 9:2 (1999), 1–24
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