01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail:
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Keywords:
second order parabolic equations; boundary-value problems; free boundary problems; existence & uniqueness of the solution; coercive estimates of the solution; weighted Holder spaces; asymptotic behavior & stabilization of the solutions.
Subject:
The unique solvability of the problems for the second order parabolic equations with the time derivative in the boundary conditions in the weighted Holder spaces is established. There is proved the existence and uniqueness of the solutions of the multi-dimensional free boundary Stefan and Florin problems in the star-shaped domains and one-dimensional Verigin, Stefan and Florin problems locally in time in the weighted Holder spaces, the coercive estimates of the solutions are obtained. Jointly with V.A.Solonnikov the unique solvability of the multi-dimensional Verigin and Stefan problems in the arbitrary domaines for the small times in the weighted Holder spaces is proved.
Biography
Graduated from Faculty of Mathematics and Mechanics of Kazakh State University in 1971 (department of the matematics physics equations). Ph.D. thesis was defended in 1982. D.Sci. thesis was defended in 1994. Professor title was received in 1997.
I am the first woman in Kazakhstan-Doctor of Sci. and Professor on mathematics.
Main publications:
Bizhanova G. I. Reshenie v vesovom prostranstve Geldera nachalno-kraevoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka s proizvodnoi po vremeni v uslovii sopryazheniya // Algebra i analiz, 1994, 6 (1), 62–92.
Bizhanova G. I. Issledovanie razreshimosti v vesovom gelderovskom prostranstve funktsii mnogomernykh dvukhfaznykh zadach Stefana i nestatsionarnoi filtratsii Florina dlya parabolicheskikh uravnenii vtorogo poryadka // Zapiski nauchnykh seminarov LOMI, 1994, 213, 14–47.
Bizhanova G. I. Reshenie v vesovom gelderovskom prostranstve funktsii mnogomernykh dvukhfaznykh zadach Stefana i Florina dlya parabolicheskikh uravnenii vtorogo poryadka v ogranichennoi oblasti // Algebra i analiz, 1995, 8 (2), 46–76.
Bizhanova G. I. O klassicheskoi razreshimosti odnomernykh zadach Florina, Masketa-Verigina i Stefana // Zapiski nauchnykh seminarov POMI, 1997, 243, 30–60.
Bizhanova G. I., Solonnikov V. A. O zadachakh so svobodnymi granitsami dlya parabolicheskikh uravnenii vtorogo poryadka // Algebra i analiz, 2000, 12 (6), 98–139. Issledovanie razreshimosti v vesovom gelderovskom prostranstve funktsii mnogomernykh dvukhfaznykh zadach Stefana i nestatsionarnoi filtratsii Florina dlya parabolicheskikh uravnenii vtorogo poryadka // Zapiski nauchnykh seminarov LOMI, 1994, 213, 14–47.
G. I. Bizhanova, “Investigation of the solvability of the first boundary – value problem for the parabolic equation under the nonfulfillment of the compatibility conditions of the initial and boundary data”, Zap. Nauchn. Sem. POMI, 508 (2021), 39–72
2018
2.
G. I. Bizhanova, “Solution of the Cauchy problem for a parabolic equation with singular coefficients”, Zap. Nauchn. Sem. POMI, 477 (2018), 35–53
2017
3.
G. I. Bizhanova, “Convergence in the Hölder space of the solutions of the problems for the parabolic equations with two small parameters in a boundary
condition”, Zap. Nauchn. Sem. POMI, 459 (2017), 7–36; J. Math. Sci. (N. Y.), 236:4 (2019), 379–398
G. I. Bizhanova, “Solution in the Hölder spaces of the free boundary problems arising in combustion theory”, Algebra i Analiz, 27:2 (2015), 42–82; St. Petersburg Math. J., 27:2 (2016), 207–235
2010
5.
G. I. Bizhanova, “Solutions in Hölder spaces of boundary-value problems for parabolic equations with nonconjugate initial and boundary data”, CMFD, 36 (2010), 12–23; Journal of Mathematical Sciences, 171:1 (2010), 9–21
G. I. Bizhanova, “Solution of a model problem related to singularly perturbed free boundaries of Stefan type”, Zap. Nauchn. Sem. POMI, 362 (2008), 64–91; J. Math. Sci. (N. Y.), 159:4 (2009), 420–435
G. I. Bizhanova, “On exact solutions of one-dimensional two phase free boundary problems for parabolic equations”, Zap. Nauchn. Sem. POMI, 318 (2004), 42–59; J. Math. Sci. (N. Y.), 136:2 (2006), 3672–3681
G. I. Bizhanova, “On solvability of H. Amann's problem in Hölder spaces”, Zap. Nauchn. Sem. POMI, 295 (2003), 18–56; J. Math. Sci. (N. Y.), 127:2 (2005), 1828–1848
G. I. Bizhanova, V. A. Solonnikov, “On problems with free boundaries for second-order parabolic equations”, Algebra i Analiz, 12:6 (2000), 98–139; St. Petersburg Math. J., 12:6 (2001), 949–981
G. I. Bizhanova, “On the classical solvability of one-dimensional free boundary Florin, Muskat–Verigin and Stefan problems”, Zap. Nauchn. Sem. POMI, 243 (1997), 30–60; J. Math. Sci. (New York), 99:1 (2000), 816–836
G. I. Bizhanova, “Solution in a weighted Hölder function space of multidimensional two-phase Stefan and Florin problems for second-order parabolic equations in a bounded domain”, Algebra i Analiz, 7:2 (1995), 46–76; St. Petersburg Math. J., 7:2 (1996), 217–241
G. I. Bizhanova, V. A. Solonnikov, “Some model problems for second-order parabolic equations with a time derivative in the boundary conditions”, Algebra i Analiz, 6:6 (1994), 30–50; St. Petersburg Math. J., 6:6 (1995), 1151–1166
G. I. Bizhanova, “Solution in a weighted Hölder space of an initial-boundary value problem for a second-order parabolic equation with a time derivative in the conjugation condition”, Algebra i Analiz, 6:1 (1994), 64–94; St. Petersburg Math. J., 6:1 (1995), 51–75
G. I. Bizhanova, “The investigation of the solvability of the multidimentional two-phase Stefan and nonstationary filtration Florin problems for the second order parabolic equations in weighted Hölder spaces of functions”, Zap. Nauchn. Sem. POMI, 213 (1994), 14–47; J. Math. Sci. (New York), 84:1 (1997), 823–844
G. I. Bizhanova, V. A. Solonnikov, “On the solvability of an initial-boundary value problem for a second-order parabolic equation with a time derivative in the boundary condition in a weighted Hölder space of functions”, Algebra i Analiz, 5:1 (1993), 109–142; St. Petersburg Math. J., 5:1 (1994), 97–124
G. I. Bizhanova, I. V. Denisova, A. I. Nazarov, K. I. Pileckas, V. V. Pukhnachev, S. I. Repin, J.-F. Rodrigues, G. A. Seregin, N. N. Uratseva, E. V. Frolova, “On the 90th birthday of Vsevolod Alekseevich Solonnikov”, Uspekhi Mat. Nauk, 78:5(473) (2023), 187–198; Russian Math. Surveys, 78:5 (2023), 971–981
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