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.
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.
