메뉴 건너뛰기




Volumn 10, Issue 12, 2005, Pages 1345-1388

Classical solutions to parabolic systems with free boundary of Stefan type

Author keywords

[No Author keywords available]

Indexed keywords


EID: 66149085404     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (3)

References (23)
  • 1
    • 0022098309 scopus 로고
    • Macroscopic global modeling of binary alloy solidification processes
    • V. Alexiades, D.G. Wilson, and A.D. Solomon, Macroscopic global modeling of binary alloy solidification processes, Quart. Appl. Math., 43 (1985), 143-158.
    • (1985) Quart. Appl. Math. , vol.43 , pp. 143-158
    • Alexiades, V.1    Wilson, D.G.2    Solomon, A.D.3
  • 2
    • 0003438193 scopus 로고
    • The Tables of Integral Transforms
    • Nauka, Moscow
    • H. Bateman and A. Erdélyi, "The Tables of Integral Transforms," Nauka, Moscow, 1969.
    • (1969)
    • Bateman, H.1    Erdélyi, A.2
  • 3
    • 0040566060 scopus 로고
    • Nonlocal Problems in the Theory of Quasilinear Parabolic Equations
    • (Russian), Novosibirsk Gos. Univ., Novosibirsk
    • V.S. Belonosov and T.I. Zelenyak, (Russian) "Nonlocal Problems in the Theory of Quasilinear Parabolic Equations," Novosibirsk Gos. Univ., Novosibirsk, 1975.
    • (1975)
    • Belonosov, V.S.1    Zelenyak, T.I.2
  • 4
    • 0000971506 scopus 로고
    • Mathematical formulation and numerical solution of an alloy solidification problem
    • (Montecatini, 1981), 237-247, Res. Notes in Math., 78, Pitman, Boston, MA
    • A. Bermudez and C. Saguez, Mathematical formulation and numerical solution of an alloy solidification problem, Free Boundary Problems: Application and Theory, Vol. I (Montecatini, 1981), 237-247, Res. Notes in Math., 78, Pitman, Boston, MA, 1983.
    • (1983) Free Boundary Problems: Application and Theory, , vol.1
    • Bermudez, A.1    Saguez, C.2
  • 5
    • 52849085312 scopus 로고
    • Estimates for the solution of an n-dimensional conjugation problem for the heat equation in weighted Hölder norms. I./II
    • (Russian), 1, 11-17.
    • G.I. Bizhanova, (Russian) Estimates for the solution of an n-dimensional conjugation problem for the heat equation in weighted Hölder norms. I./II, Izv. Akad. Nauk Kaz.SSR. Ser. Fiz.-Mat. (1992), 5, 7-13; (1993), 1, 11-17.
    • (1992) Izv. Akad. Nauk Kaz.SSR. Ser. Fiz.-Mat. , vol.5 , pp. 7-13
    • Bizhanova, G.I.1
  • 6
    • 18144373390 scopus 로고
    • Investigation of the solvability in a weighted Hölder function space of the multidimensional two-phase Stefan problem and the multidimensional Florin nonstationary filtration problem for second-order parabolic equations (Cauchy-Stefan and Cauchy-Florin problems)
    • translation in J. Math. Sci. (New York), 84(1) (1997), 823-844.
    • G.I. Bizhanova, Investigation of the solvability in a weighted Hölder function space of the multidimensional two-phase Stefan problem and the multidimensional Florin nonstationary filtration problem for second-order parabolic equations (Cauchy-Stefan and Cauchy-Florin problems), Zap. Nauchn. Sem. St. Petersburg Otdel. Mat. Inst. Steklov (POMI), 213 (1994), 14-47; translation in J. Math. Sci. (New York), 84(1) (1997), 823-844.
    • (1994) Zap. Nauchn. Sem. St. Petersburg Otdel. Mat. Inst. Steklov (POMI) , vol.213 , pp. 14-47
    • Bizhanova, G.I.1
  • 7
    • 0141684628 scopus 로고
    • 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
    • translation in St. Petersburg Math. J., 6(1) (1995), 51-75.
    • 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; translation in St. Petersburg Math. J., 6(1) (1995), 51-75.
    • (1994) Algebra i Analiz , vol.6 , Issue.1 , pp. 64-94
    • Bizhanova, G.I.1
  • 8
    • 34249949227 scopus 로고
    • Solution in a weighted Hölder function space of multidimensional twophase Stefan and Florin problems for second-order parabolic equations in a bounded domain
    • translation in St. Petersburg Math. J., 7(2) (1996), 217-241.
    • G.I. Bizhanova, Solution in a weighted Hölder function space of multidimensional twophase Stefan and Florin problems for second-order parabolic equations in a bounded domain, Algebra i Analiz, 7(2) (1995), 46-76; translation in St. Petersburg Math. J., 7(2) (1996), 217-241.
    • (1995) Algebra i Analiz , vol.7 , Issue.2 , pp. 46-76
    • Bizhanova, G.I.1
  • 9
    • 18144413479 scopus 로고    scopus 로고
    • On problems with free boundaries for secondorder parabolic equations
    • translation in St.Petersburg Math. J., 12(6) (2001), 949-981.
    • G.I. Bizhanova and V.A. Solonnikov, On problems with free boundaries for secondorder parabolic equations, Algebra i Analiz, 12(6) (2000), 98-139; translation in St.Petersburg Math. J., 12(6) (2001), 949-981.
    • (2000) Algebra i Analiz , vol.12 , Issue.6 , pp. 98-139
    • Bizhanova, G.I.1    Solonnikov, V.A.2
  • 10
    • 0018480579 scopus 로고
    • On the numerical solution of an alloy solidification problem
    • A.B. Crowley and J.R. Ockendon, On the numerical solution of an alloy solidification problem, Int. J. Heat Mass Transfer, 22 (1979), 941-947.
    • (1979) Int. J. Heat Mass Transfer , vol.22 , pp. 941-947
    • Crowley, A.B.1    Ockendon, J.R.2
  • 11
    • 84971928337 scopus 로고
    • On the correctness of a model for phase transitions in binary alloys
    • I.G. Götz, On the correctness of a model for phase transitions in binary alloys, European J. Appl. Math., 1(4) (1990), 327-338.
    • (1990) European J. Appl. Math. , vol.1 , Issue.4 , pp. 327-338
    • Götz, I.G.1
  • 12
    • 84972561749 scopus 로고
    • Classical solutions of the Stefan problem
    • E.I. Hanzawa, Classical solutions of the Stefan problem, Tohoku Math. J., 33 (1981), 297-335.
    • (1981) Tohoku Math. J. , vol.33 , pp. 297-335
    • Hanzawa, E.I.1
  • 13
    • 0003690985 scopus 로고
    • Linear and quasilinear equations of parabolic type, "Nauka"
    • Moscow translation by S. Smith, Translations of Mathematical Monographs, American Mathematical Society, Providence, R.I. 1967
    • O.A. Ladyženskaja, V.A. Solonnikov, and N.N. Ural'çeva, Linear and quasilinear equations of parabolic type, "Nauka", Moscow, 1967; translation by S. Smith, Translations of Mathematical Monographs, Vol. 23 American Mathematical Society, Providence, R.I. 1967.
    • (1967) , vol.23
    • Ladyženskaja, O.A.1    Solonnikov, V.A.2    Ural'çeva, N.N.3
  • 14
    • 0003492651 scopus 로고    scopus 로고
    • Second Order Parabolic Differential Equations
    • World Scientific Publishing Co., Inc., River Edge, NJ
    • Gary M. Lieberman, "Second Order Parabolic Differential Equations," World Scientific Publishing Co., Inc., River Edge, NJ, 1996.
    • (1996)
    • Lieberman, G.M.1
  • 15
    • 0001265748 scopus 로고
    • The classical solution of a multidimensional Stefan problem for quasilinear parabolic equations
    • 2(6)
    • A.M. Meirmanov, The classical solution of a multidimensional Stefan problem for quasilinear parabolic equations, Mat. Sbornik (N.S.), 112(154) (1980), 2(6), 170-192.
    • (1980) Mat. Sbornik (N.S.) , vol.112 , Issue.154 , pp. 170-192
    • Meirmanov, A.M.1
  • 16
    • 0003892889 scopus 로고
    • The Stefan Problem
    • Walter de Gruyter & Co., Berlin
    • A.M. Meirmanov, "The Stefan Problem," Walter de Gruyter & Co., Berlin, 1992.
    • (1992)
    • Meirmanov, A.M.1
  • 17
    • 84894387805 scopus 로고
    • Local solvability of the Stefan thermodiffusion problem
    • (Russian)
    • A.G. Petrova, (Russian) Local solvability of the Stefan thermodiffusion problem, Dinamika Sploshn. Sredy, 58 (1982), 156-163.
    • (1982) Dinamika Sploshn. Sredy , vol.58 , pp. 156-163
    • Petrova, A.G.1
  • 18
    • 0033413774 scopus 로고    scopus 로고
    • On a parabolic system with time derivative in the boundary conditions and related free boundary problems
    • J.F. Rodrigues, V.A. Solonnikov, and F. Yi, On a parabolic system with time derivative in the boundary conditions and related free boundary problems, Math. Ann., 315 (1999), 61-95.
    • (1999) Math. Ann. , vol.315 , pp. 61-95
    • Rodrigues, J.F.1    Solonnikov, V.A.2    Yi, F.3
  • 19
    • 0003814972 scopus 로고
    • The Stefan Problem
    • translation by A.D. Solomon, Translations of Mathematical Monographs, Vol. 27, American Mathematical Society, Providence, R.I.
    • L.I. Rubinstein, "The Stefan Problem," translation by A.D. Solomon, Translations of Mathematical Monographs, Vol. 27, American Mathematical Society, Providence, R.I., 1971.
    • (1971)
    • Rubinstein, L.I.1
  • 21
    • 67349189068 scopus 로고
    • On an estimate of the maximum of a derivative modulus for a solution of a uniform parabolic initial-boundary value problem
    • (Russian) LOMI Preprint No. P-2-77
    • V.A. Solonnikov, (Russian) On an estimate of the maximum of a derivative modulus for a solution of a uniform parabolic initial-boundary value problem, LOMI Preprint No. P-2-77, 1977.
    • (1977)
    • Solonnikov, V.A.1
  • 22
    • 24944590549 scopus 로고    scopus 로고
    • Lectures on evolution free boundary problems: classical solutions, Mathematical aspects of evolving interfaces (Funchal, 2000)
    • Springer, Berlin
    • V.A. Solonnikov, Lectures on evolution free boundary problems: classical solutions, Mathematical aspects of evolving interfaces (Funchal, 2000), 123-175, Lecture Notes in Math., 1812, Springer, Berlin, 2003.
    • (2003) Lecture Notes in Math. , vol.1812 , pp. 123-175
    • Solonnikov, V.A.1
  • 23
    • 0003768048 scopus 로고    scopus 로고
    • Models of Phase Transitions
    • Birkhuser Boston, Inc., Boston, MA
    • A. Visintin, "Models of Phase Transitions," Birkhuser Boston, Inc., Boston, MA, 1996.
    • (1996)
    • Visintin, A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.