References
G. A. Sviridyuk, “The Cauchy problem for a singular linear operator equation of Sobolev type,” Differentsial'nye Uravneniya,23, No. 12, 2168–2171 (1987).
G. A. Sviridyuk, “Manifolds of solutions to a class of equations of evolution and dynamics,” Dokl. Akad. Nauk SSSR,304, No. 2, 301–304 (1989).
D. Henry, Geometric Theory of Semilinear Parabolic Equations [Russian translation], Mir, Moscow (1985).
T. Kato, Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).
K. Yosida, Functional Analysis [Russian translation], Mir, Moscow (1967).
G. A. Sviridyuk and M. V. Sukhanova, “Solvability of the Cauchy problem for singular linear equations of evolution type,” Differentsial'nye Uravneniya,28, No. 3, 508–515 (1992).
G. A. Sviridyuk, Study of Semilinear Equations of Sobolev Type in Banach Spaces [in Russian], Dis. Dokt. Fiz.-Mat. Nauk, Chelyabinsk (1992).
G. A. Sviridyuk, “Semilinear equations of Sobolev type with relatively sectorial operators,” Dokl. Akad. Nauk SSSR,329, No. 3, 274–277 (1993).
G. A. Sviridyuk and T. G. SukachËva, “Phase spaces for a class of semilinear equations of Sobolev type,” Differentsial'nye Uravneniya,26, No. 2, 250–258 (1990).
G. A. Sviridyuk and T. G. SukachËva, “The Cauchy problem for a class of semilinear equations of Sobolev type,” Sibirsk. Mat. Zh.,31, No. 5, 109–119 (1990).
G. A. Sviridyuk, “The manifold of solutions to a singular pseudoparabolic operator equation,” Dokl. Akad. Nauk SSSR,289, No. 6, 1315–1318 (1986).
G. A. Sviridyuk, “Some problem for the generalized Boussinesq filtration equation,” Izv. Vyssh. Uchebn. Zaved. Matematika, No. 2, 55–61 (1989).
G. A. Sviridyuk, “Quasistationary trajectories of semilinear dynamical equations of Sobolev type,” Izv. RAN Ser. Mat.,57, No. 3, 192–207 (1993).
G. A. Sviridyuk, “Sobolev-type semilinear equations with a relatively bounded operator,” Dokl. Akad. Nauk SSSR,318, No. 4, 828–831 (1991).
R. E. Showalter, “Nonlinear degenerate evolution equations and partial differential equations of mixed type,” SIAM J. Math. Anal.,6, No. 1, 25–42 (1975).
N. A. Sidorov, “On a class of degenerate differential equations with convergence,” Mat. Zametki,35, No. 4, 569–578 (1984).
G. A. Sviridyuk, “On a problem by Showalter,” Differentsial'nye Uravneniya,25, No. 2, 338–339 (1989).
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The research was partially supported by the “Russian Universities” program within the section “Fundamental Problems of Mathematics and Mechanics” (Grant 1.5.16).
Translated fromSibirskii Matematicheskio Zhurnal, Vol. 36, No. 5, pp. 1130–1145, September–October, 1995.
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Sviridyuk, G.A., FËdorov, V.E. Analytic semigroups with kernel and linear equations of Sobolev type. Sib Math J 36, 973–987 (1995). https://doi.org/10.1007/BF02112539
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DOI: https://doi.org/10.1007/BF02112539