Literature Cited
S. L. Sobolev, “A new problem of mathematical physics,” Izv. Akad. Nauk SSSR, Ser. Mat.,18, 3–50 (1954).
S. G. Krein and K. I. Chernyshov, “Singular perturbed differential equations in a Banach space,” Preprint, Inst. Mat., Akad. Nauk SSSR, Sib. Branch, Novosibirsk (1979).
S. P. Zubova and K. I. Chernyshov, “Linear differential equation with Fredholm operator for the derivative,” Differents. Uravnen. Prilozhen.,14, 21–39 (1976).
N. A. Sidorov and O. A. Romanova, “Application of results of branching theory for the solution of degenerate differential equations,” Differents. Uravnen.,19, No. 9, 1516–1526 (1983).
A. P. Oskolkov, “Initial-boundary problems for equations of motion of a Kelvin-Voight fluid and an Oldroyd fluid,” Tr. Mat. Inst. Akad. Nauk SSSR, No. 179, 126–164 (1988).
G. A. Sviridyuk, “Manifolds of solutions of a class of evolution and dynamic equations,” Dokl. Akad. Nauk SSSR,304 No. 2, 301–304 (1989).
G. A. Sviridyuk, “Cauchy problem for a singular equation of Sobolev type,” Differents. Uravnen.,23, no. 12, 2169–2171 (1987).
G. A. Sviridyuk, “Manifold of solutions of a problem of the dynamics of an incompressible viscoelastic fluid,” Differents. Uravnen.,24, No. 10, 1846–1848 (1988).
V. I. Arnol'd, V. S. Afraimovich, Yu S. Il'yashenko, and L. P. Shil'nikov, “Theory of bifurcations,” Itogi Nauki Tekhniki, Seriya Sovremennye Problemy Matematiki, Fundamental'nye Napravleniya,5 (1986).
G. V. Vinogradov and A. Ya. Malkin, Rheology of Polymers [in Russian], Khiniya, Moscow (1977).
S. Lang, Introduction to the Theory of Differentiable Manifolds [Russian translation], Mir, Moscow (1967).
G. A. Sviridyuk, “A model of the dynamics of an incompressible viscoelastic fluid,” Izv. Vuzov. Matematika, No. 1, 74–79 (1988).
V. A. Solonnikov, “Estimates of Green's tensors for some boundary problems,” Dokl. Akad. Nauk SSSR,130, No. 5, 988–991 (1960).
I. I. Vorovich and V. I. Yudovich, “Stationary flows of a viscous incompressible fluid,” Mat. Sborn.,51, No. 2, 393–428 (1961).
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Chelyabinsk. Novgorod. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 31, No. 5, pp. 109–119, September–October, 1990.
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Sviridyuk, G.A., Sukacheva, T.G. Cauchy problem for a class of semilinear equations of Sobolev type. Sib Math J 31, 794–802 (1990). https://doi.org/10.1007/BF00974493
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DOI: https://doi.org/10.1007/BF00974493