Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
E-mail: ,
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.
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.
