메뉴 건너뛰기




Volumn 49, Issue 6, 2017, Pages 4942-5006

Local well-posedness and global stability of the two-phase stefan problem

Author keywords

Free boundary problem; Interface motion; Stefan problem; Two phase problem

Indexed keywords

MATHEMATICAL MODELS;

EID: 85040043925     PISSN: 00361410     EISSN: 10957154     Source Type: Journal    
DOI: 10.1137/16M1083207     Document Type: Article
Times cited : (9)

References (51)
  • 1
    • 0030536801 scopus 로고    scopus 로고
    • Caloric functions in lipschitz domains and the regularity of solutions to phase transition problems
    • I. Athanasopoulos, L. Caffarelli, and S. Salsa, Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Ann. of Math. (2), 143 (1996), pp. 413-434.
    • (1996) Ann. of Math , vol.143 , Issue.2 , pp. 413-434
    • Athanasopoulos, I.1    Caffarelli, L.2    Salsa, S.3
  • 2
    • 0001055847 scopus 로고    scopus 로고
    • Regularity of the free boundary in parabolic phase-Transition problems
    • I. Athanasopoulos, L. Caffarelli, and S. Salsa, Regularity of the free boundary in parabolic phase-Transition problems, Acta Math., 176 (1996), pp. 245-282.
    • (1996) Acta Math. , vol.176 , pp. 245-282
    • Athanasopoulos, I.1    Caffarelli, L.2    Salsa, S.3
  • 3
    • 0040117095 scopus 로고    scopus 로고
    • Phase transition problems of parabolic type: Flat free boundaries are smooth
    • I. Athanasopoulos, L. A. Caffarelli, and S. Salsa, Phase transition problems of parabolic type: Flat free boundaries are smooth, Comm. Pure Appl. Math., 51 (1998), pp. 77-112.
    • (1998) Comm. Pure Appl. Math , vol.51 , pp. 77-112
    • Athanasopoulos, I.1    Caffarelli, L.A.2    Salsa, S.3
  • 5
    • 33947704957 scopus 로고    scopus 로고
    • A geometric approach to free boundary problems
    • AMS, Providence, RI
    • L. Caffarelli and S. Salsa, A Geometric Approach to Free Boundary Problems, Grad. Stud. Math. 68, AMS, Providence, RI, 2005.
    • (2005) Grad. Stud. Math , vol.68
    • Caffarelli, L.1    Salsa, S.2
  • 6
    • 0000409224 scopus 로고
    • The regularity of free boundaries in higher dimensions
    • L. A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math., 139 (1977), pp. 155-184.
    • (1977) Acta Math , vol.139 , pp. 155-184
    • Caffarelli, L.A.1
  • 7
    • 0042295929 scopus 로고
    • Some aspects of the one-phase stefan problem
    • L. A. Caffarelli, Some aspects of the one-phase Stefan problem, Indiana Univ. Math. J., 27 (1978), pp. 73-77.
    • (1978) Indiana Univ. Math. J , vol.27 , pp. 73-77
    • Caffarelli, L.A.1
  • 8
    • 0020549958 scopus 로고
    • Continuity of the temperature in the two-phase stefan problem
    • L. A. Caffarelli and L. C. Evans, Continuity of the temperature in the two-phase Stefan problem, Arch. Ration. Mech. Anal., 81 (1983), pp. 199-220.
    • (1983) Arch. Ration. Mech. Anal , vol.81 , pp. 199-220
    • Caffarelli, L.A.1    Evans, L.C.2
  • 9
    • 0042295981 scopus 로고
    • Continuity of the temperature in the stefan problem
    • L. A. Caffarelli and A. Friedman, Continuity of the temperature in the Stefan problem, Indiana Univ. Math. J., 28 (1979), pp. 53-70.
    • (1979) Indiana Univ. Math. J , vol.28 , pp. 53-70
    • Caffarelli, L.A.1    Friedman, A.2
  • 10
    • 84907584396 scopus 로고    scopus 로고
    • Global existence and decay for solutions of the hele-shaw flow with injection
    • C. H. A. Cheng, D. Coutand, and S. Shkoller, Global existence and decay for solutions of the Hele-Shaw flow with injection, Interfaces Free Bound., 16 (2014), pp. 297-338.
    • (2014) Interfaces Free Bound , vol.16 , pp. 297-338
    • Cheng, C.H.A.1    Coutand, D.2    Shkoller, S.3
  • 11
    • 84942354084 scopus 로고    scopus 로고
    • Well-posedness of the muskat problem with H2 initial data
    • C. H. A. Cheng, R. Granero-Belinchón, and S. Shkoller, Well-posedness of the Muskat problem with H2 initial data, Adv. Math., 286 (2016), pp. 32-104.
    • (2016) Adv. Math , vol.286 , pp. 32-104
    • Cheng, C.H.A.1    Granero-Belinchón, R.2    Shkoller, S.3
  • 12
    • 78650916026 scopus 로고    scopus 로고
    • Regularity of one-phase stefan problem near lipschitz initial data
    • S. Choi and I. C. Kim, Regularity of one-phase Stefan problem near Lipschitz initial data, Amer. J. Math., 132 (2010), pp. 1693-1727.
    • (2010) Amer. J. Math , vol.132 , pp. 1693-1727
    • Choi, S.1    Kim, I.C.2
  • 13
    • 84878893542 scopus 로고    scopus 로고
    • The two-phase stefan problem: Regularization near lipschitz initial data by phase dynamics
    • S. Choi and I. C. Kim, The two-phase Stefan problem: Regularization near Lipschitz initial data by phase dynamics, Anal. PDE, 5 (2012), pp. 1063-1103.
    • (2012) Anal. PDE , vol.5 , pp. 1063-1103
    • Choi, S.1    Kim, I.C.2
  • 14
    • 78751624212 scopus 로고    scopus 로고
    • Interface evolution: The hele-shaw and muskat problems
    • A. Córdoba, D. Córdoba, and F. Gancedo, Interface evolution: The Hele-Shaw and Muskat problems, Ann. of Math. (2), 173 (2011), pp. 477-542.
    • (2011) Ann. of Math , vol.173 , Issue.2 , pp. 477-542
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 15
    • 30144444877 scopus 로고    scopus 로고
    • The interaction between quasilinear elastodynamics and the navier-stokes equations
    • D. Coutand and S. Shkoller, The interaction between quasilinear elastodynamics and the Navier-Stokes equations, Arch. Ration. Mech. Anal., 179 (2006), pp. 303-352.
    • (2006) Arch. Ration. Mech. Anal , vol.179 , pp. 303-352
    • Coutand, D.1    Shkoller, S.2
  • 16
    • 34548446988 scopus 로고    scopus 로고
    • Well-posedness of the free-surface incompressible euler equations with or without surface tension
    • D. Coutand and S. Shkoller, Well-posedness of the free-surface incompressible Euler equations with or without surface tension, J. Amer. Math. Soc., 20 (2007), pp. 829-930.
    • (2007) J. Amer. Math. Soc , vol.20 , pp. 829-930
    • Coutand, D.1    Shkoller, S.2
  • 17
    • 84864603441 scopus 로고    scopus 로고
    • A simple proof of well-posedness for the free-surface incompressible euler equations
    • D. Coutand and S. Shkoller, A simple proof of well-posedness for the free-surface incompressible Euler equations, Discrete Contin. Dyn. Syst. Ser. S, 3 (2010), pp. 429-449.
    • (2010) Discrete Contin. Dyn. Syst. Ser. S , vol.3 , pp. 429-449
    • Coutand, D.1    Shkoller, S.2
  • 18
    • 78650229802 scopus 로고    scopus 로고
    • Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum
    • D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for moving-boundary 1-D compressible Euler equations in physical vacuum, Comm. Pure Appl. Math., 64 (2011), pp. 328-366.
    • (2011) Comm. Pure Appl. Math , vol.64 , pp. 328-366
    • Coutand, D.1    Shkoller, S.2
  • 19
    • 84870334285 scopus 로고    scopus 로고
    • Well-posedness in smooth function spaces for moving-boundary 3-D compressible euler equations in physical vacuum
    • D. Coutand and S. Shkoller, Well-posedness in smooth function spaces for moving-boundary 3-D compressible Euler equations in physical vacuum, Arch. Ration. Mech. Anal., 2012.
    • (2012) Arch. Ration. Mech. Anal
    • Coutand, D.1    Shkoller, S.2
  • 20
    • 84891662791 scopus 로고    scopus 로고
    • On the finite-Time splash and splat singularities for the 3-D free-surface Euler equations
    • D. Coutand and S. Shkoller, On the finite-Time splash and splat singularities for the 3-D free-surface Euler equations, Comm. Math. Phys., 325 (2014), pp. 143-183.
    • (2014) Comm. Math. Phys , vol.325 , pp. 143-183
    • Coutand, D.1    Shkoller, S.2
  • 21
    • 84959109234 scopus 로고    scopus 로고
    • On the impossibility of finite-Time splash singularities for vortex sheets
    • D. Coutand and S. Shkoller, On the impossibility of finite-Time splash singularities for vortex sheets, Arch. Ration. Mech. Anal., 221 (2016), pp. 987-1033.
    • (2016) Arch. Ration. Mech. Anal , vol.221 , pp. 987-1033
    • Coutand, D.1    Shkoller, S.2
  • 22
    • 1642320714 scopus 로고    scopus 로고
    • All time smooth solutions of the one-phase stefan problem and the hele-shaw flow
    • P. Daskalopoulos and K. Lee, All time smooth solutions of the one-phase Stefan problem and the Hele-Shaw flow, Comm. Partial Differential Equations, 29 (2004), pp. 71-89.
    • (2004) Comm. Partial Differential Equations , vol.29 , pp. 71-89
    • Daskalopoulos, P.1    Lee, K.2
  • 23
    • 0011555392 scopus 로고
    • The equations of motion of a perfect fluid with free boundary are not well posed
    • D. G. Ebin, The equations of motion of a perfect fluid with free boundary are not well posed, Comm. Partial Differential Equations, 12 (1987), pp. 1175-1201.
    • (1987) Comm. Partial Differential Equations , vol.12 , pp. 1175-1201
    • Ebin, D.G.1
  • 24
    • 84968481497 scopus 로고
    • The stefan problem in several space variables
    • A. Friedman, The Stefan problem in several space variables, Trans. Amer. Math. Soc., 133 (1968), pp. 51-87.
    • (1968) Trans. Amer. Math. Soc , vol.133 , pp. 51-87
    • Friedman, A.1
  • 27
    • 34249940988 scopus 로고    scopus 로고
    • Lp-Theory for the stefan problem
    • E. V. Frolova and V. A. Solonnikov, Lp-Theory for the Stefan problem, J. Math. Sci., 373 (2000), pp. 989-1006.
    • (2000) J. Math. Sci , vol.373 , pp. 989-1006
    • Frolova, E.V.1    Solonnikov, V.A.2
  • 28
    • 84856727335 scopus 로고    scopus 로고
    • Orthogonality conditions and asymptotic stability in the stefan problem with surface tension
    • M. Hadžić, Orthogonality conditions and asymptotic stability in the Stefan problem with surface tension, Arch. Ration. Mech. Anal., 203 (2012), pp. 719-745.
    • (2012) Arch. Ration. Mech. Anal , vol.203 , pp. 719-745
    • Hadžić, M.1
  • 29
    • 77950944473 scopus 로고    scopus 로고
    • Stability in the stefan problem with surface tension (i)
    • M. Hadžić and Y. Guo, Stability in the Stefan problem with surface tension (I), Comm. Partial Differential Equations, 35 (2010), pp. 201-244.
    • (2010) Comm. Partial Differential Equations , vol.35 , pp. 201-244
    • Hadžić, M.1    Guo, Y.2
  • 30
    • 84995810972 scopus 로고    scopus 로고
    • Well-posedness for the classical stefan problem and the zero surface tension limit
    • M. Hadžić and S. Shkoller, Well-posedness for the classical Stefan problem and the zero surface tension limit, Arch. Ration. Mech. Anal., 223 (2017), pp. 213-264.
    • (2017) Arch. Ration. Mech. Anal , vol.223 , pp. 213-264
    • Hadžic, M.1    Shkoller, S.2
  • 31
    • 84925437918 scopus 로고    scopus 로고
    • Global stability and decay for the classical stefan problem
    • M. Hadžić and S. Shkoller, Global stability and decay for the classical Stefan problem, Comm. Pure Appl. Math., 68 (2015), pp. 689-757.
    • (2015) Comm. Pure Appl. Math , vol.68 , pp. 689-757
    • Hadžic, M.1    Shkoller, S.2
  • 32
    • 84939207213 scopus 로고    scopus 로고
    • Global stability of steady states in the classical stefan problem for general boundary shapes
    • M. Hadžić and S. Shkoller, Global stability of steady states in the classical Stefan problem for general boundary shapes, Philos. Trans. A, 373 (2015), 20140284.
    • (2015) Philos. Trans. A , vol.373 , pp. 20140284
    • Hadžic, M.1    Shkoller, S.2
  • 33
    • 84972561749 scopus 로고
    • Classical solutions of the stefan problem
    • E. Hanzawa, Classical solutions of the Stefan problem, Tôhoku Math. J. (2), 33 (1981), pp. 297-335.
    • (1981) Tôhoku Math. J , vol.33 , Issue.2 , pp. 297-335
    • Hanzawa, E.1
  • 35
    • 0043245213 scopus 로고    scopus 로고
    • Uniqueness and existence results on the hele-shaw and the stefan problems
    • I. C. Kim, Uniqueness and existence results on the Hele-Shaw and the Stefan problems, Arch. Ration. Mech. Anal., 168 (2003), pp. 299-328.
    • (2003) Arch. Ration. Mech. Anal , vol.168 , pp. 299-328
    • Kim, I.C.1
  • 36
    • 78649488616 scopus 로고    scopus 로고
    • Viscosity solutions for the two-phase stefan problem
    • I. C. Kim and N. Požár, Viscosity solutions for the two-phase Stefan problem, Comm. Partial Differential Equations, 36 (2011), pp. 42-66.
    • (2011) Comm. Partial Differential Equations , vol.36 , pp. 42-66
    • Kim, I.C.1    Požár, N.2
  • 38
    • 84980156672 scopus 로고
    • The smoothness of the free boundary in the one phase stefan problem
    • D. Kinderlehrer and L. Nirenberg, The smoothness of the free boundary in the one phase Stefan problem, Comm. Pure Appl. Math., 31 (1978), pp. 257-282.
    • (1978) Comm. Pure Appl. Math , vol.31 , pp. 257-282
    • Kinderlehrer, D.1    Nirenberg, L.2
  • 39
    • 0003295459 scopus 로고
    • An introduction to variational inequalities and their applications
    • Academic Press, New York
    • D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Pure Appl. Math. 88, Academic Press, New York, 1980.
    • (1980) Pure Appl. Math , vol.88
    • Kinderlehrer, D.1    Stampacchia, G.2
  • 40
    • 0346934116 scopus 로고    scopus 로고
    • Classical solutions to phase transition problems are smooth
    • H. Koch, Classical solutions to phase transition problems are smooth, Comm. Partial Differential Equations, 23 (1998), pp. 389-437.
    • (1998) Comm. Partial Differential Equations , vol.23 , pp. 389-437
    • Koch, H.1
  • 42
    • 0020703936 scopus 로고
    • Bifurcation and optimal stochastic control
    • P.-L. Lions, Bifurcation and optimal stochastic control, Nonlinear Anal., 7 (1983), pp. 177-207.
    • (1983) Nonlinear Anal , vol.7 , pp. 177-207
    • Lions, P.-L.1
  • 43
    • 0002708047 scopus 로고
    • The stefan problem
    • Walter de Gruyter, Berlin
    • A. M. Meirmanov, The Stefan Problem, De Gruyter Exp. Math. 3, Walter de Gruyter, Berlin, 1992.
    • (1992) De Gruyter Exp. Math , vol.3
    • Meirmanov, A.M.1
  • 44
    • 34249936488 scopus 로고    scopus 로고
    • Existence of analytic solutions for the classical stefan problem
    • J. Prüss, J. Saal, and G. Simonett, Existence of analytic solutions for the classical Stefan problem, Math. Ann., 338 (2007), pp. 703-755.
    • (2007) Math. Ann , vol.338 , pp. 703-755
    • Prüss, J.1    Saal, J.2    Simonett, G.3
  • 45
    • 84872192587 scopus 로고    scopus 로고
    • Qualitative behavior of solutions for thermodynamically consistent stefan problems with surface tension
    • J. Prüss, G. Simonett, and R. Zacher, Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension, Arch. Ration. Mech. Anal., 207 (2013), pp. 611-667.
    • (2013) Arch. Ration. Mech. Anal , vol.207 , pp. 611-667
    • Prüss, J.1    Simonett, G.2    Zacher, R.3
  • 46
    • 23044524517 scopus 로고    scopus 로고
    • Asymptotic convergence of the stefan problem to hele-shaw
    • F. Quirós and J. L. Vázquez, Asymptotic convergence of the Stefan problem to Hele-Shaw, Trans. Amer. Math. Soc., 353 (2001), pp. 609-634.
    • (2001) Trans. Amer. Math. Soc , vol.353 , pp. 609-634
    • Quirós, F.1    Vázquez, J.L.2
  • 47
    • 0003341014 scopus 로고
    • The stefan problem
    • AMS, Providence, RI
    • L. I. Rubenstein, The Stefan Problem, Transl. Math. Monogr. 27, AMS, Providence, RI, 1971.
    • (1971) Transl. Math. Monogr , vol.27
    • Rubenstein, L.I.1
  • 48
    • 0005429898 scopus 로고
    • ÜBer die theorie der eisbildung, insbesondere über die eisbildung im polarmeere, sitzungs-berichteder osterreichischen akad. Wiss. Math. Naturwissen-schaftliche klasse, abteilung
    • J. Stefan, Über die theorie der eisbildung, insbesondere über die eisbildung im polarmeere, Sitzungs-berichteder Osterreichischen Akad. Wiss. Math. Naturwissen-schaftliche Klasse, Abteilung 2, Math. Astron. Phys. Meteorol. Tech., 98 (1889), pp. 965-983.
    • (1889) Math. Astron. Phys. Meteorol. Tech , vol.2 , Issue.98 , pp. 965-983
    • Stefan, J.1
  • 49
    • 84944482877 scopus 로고
    • ÜBer die theorie der eisbildung, insbesondere über die eisbildung im polarmeere
    • J. Stefan, Über die theorie der eisbildung, insbesondere über die eisbildung im polarmeere, Ann. Phys, Chem., 42 (1891), pp. 269-286.
    • (1891) Ann. Phys, Chem , vol.42 , pp. 269-286
    • Stefan, J.1
  • 51
    • 0033446356 scopus 로고
    • Well-posedness in sobolev spaces of the full water wave problem in 3-D
    • S. Wu, Well-posedness in Sobolev spaces of the full water wave problem in 3-D, J. Amer. Math. Soc., 12 (1990), pp. 445-495.
    • (1990) J. Amer. Math. Soc , vol.12 , pp. 445-495
    • Wu, S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.