[1]

U. G. Abdulla,
On the optimal control of the free boundary problems for the second order parabolic equations. I. Well-posedness and convergence of the method of lines,
Inverse Probl. Imaging 7 (2013), no. 2, 307–340.
CrossrefWeb of ScienceGoogle Scholar

[2]

U. G. Abdulla,
On the optimal control of the free boundary problems for the second order parabolic equations. II. Convergence of the method of finite differences,
Inverse Probl. Imaging 10 (2016), no. 4, 869–898.
Web of ScienceCrossrefGoogle Scholar

[3]

J. Baumeister,
Zur optimalen Steuerung von freien Randwertaufgaben,
Z. Angew. Math. Mech. 60 (1980), no. 7, T333–T335.
Google Scholar

[4]

J. B. Bell,
The noncharacteristic Cauchy problem for a class of equations with time dependence. I. Problems in one space dimension,
SIAM J. Math. Anal. 12 (1981), no. 5, 759–777.
CrossrefGoogle Scholar

[5]

O. V. Besov, V. P. Il’in and S. M. Nikol’skiĭ,
Integral Representations of Functions and Imbedding Theorems. Vol. 1,
John Wiley & Sons, Hoboken, 1979.
Google Scholar

[6]

O. V. Besov, V. P. Il’in and S. M. Nikol’skiĭ,
Integral Representations of Functions and Imbedding Theorems. Vol. 2,
John Wiley & Sons, Hoboken, 1979.
Google Scholar

[7]

B. M. Budak and V. N. Vasil’eva,
On the solution of the inverse Stefan problem,
Sov. Math. Dokl. 13 (1972), 811–815.
Google Scholar

[8]

B. M. Budak and V. N. Vasil’eva,
Solution of the inverse Stefan problem (in Russian),
Ž. Vyčisl. Mat. i Mat. Fiz. 13 (1973), 103–118, 268.
Google Scholar

[9]

B. M. Budak and V. N. Vasil’eva,
Solution of the inverse Stefan problem. II (in Russian),
Ž. Vyčisl. Mat. i Mat. Fiz. 13 (1973), 897–906, 1090.
Google Scholar

[10]

J. R. Cannon,
A Cauchy problem for the heat equation,
Ann. Mat. Pura Appl. (4) 66 (1964), 155–165.
CrossrefGoogle Scholar

[11]

J. R. Cannon and J. Douglas, Jr.,
The Cauchy problem for the heat equation,
SIAM J. Numer. Anal. 4 (1967), 317–336.
CrossrefGoogle Scholar

[12]

A. Carasso,
Determining surface temperatures from interior observations,
SIAM J. Appl. Math. 42 (1982), no. 3, 558–574.
CrossrefGoogle Scholar

[13]

R. E. Ewing,
The Cauchy problem for a linear parabolic partial differential equation,
J. Math. Anal. Appl. 71 (1979), no. 1, 167–186.
CrossrefGoogle Scholar

[14]

R. E. Ewing and R. S. Falk,
Numerical approximation of a Cauchy problem for a parabolic partial differential equation,
Math. Comp. 33 (1979), no. 148, 1125–1144.
CrossrefGoogle Scholar

[15]

A. Fasano and M. Primicerio,
General free-boundary problems for the heat equation. I,
J. Math. Anal. Appl. 57 (1977), no. 3, 694–723.
CrossrefGoogle Scholar

[16]

N. L. Gol’dman,
Inverse Stefan Problems,
Kluwer Academic, Dodrecht, 1997.
Google Scholar

[17]

K.-H. Hoffman and M. Niezgodka,
Control of parabolic systems involving free boundaries,
Free Boundary Problems. Vol. 2,
Pitman Research Notes in Math. 79,
Pitman, Boston (1983), 431–462.
Google Scholar

[18]

K.-H. Hoffman and J. Sprekels,
Real-time control of the free boundary in a two-phase Stefan problem,
Numer. Funct. Anal. Optim. 5 (1982), no. 1, 47–76.
CrossrefGoogle Scholar

[19]

K.-H. Hoffmann and J. Sprekels,
On the identification of heat conductivity and latent heat in a one-phase Stefan problem,
Control Cybernet. 14 (1985), no. 1–3, 37–51.
Google Scholar

[20]

P. Jochum,
The inverse Stefan problem as a problem of nonlinear approximation theory,
J. Approx. Theory 30 (1980), no. 2, 81–98.
CrossrefGoogle Scholar

[21]

P. Jochum,
The numerical solution of the inverse Stefan problem,
Numer. Math. 34 (1980), no. 4, 411–429.
CrossrefGoogle Scholar

[22]

A. D. Juriĭ,
An optimal problem of Stefan type,
Dokl. Akad. Nauk SSSR 251 (1980), no. 6, 1317–1321.
Google Scholar

[23]

P. Knabner,
Stability theorems for general free boundary problems of the Stefan type and applications,
Applied Nonlinear Functional Analysis (Berlin 1981),
Methoden Verfahren Math. Phys. 25,
Lang, Frankfurt (1983), 95–116.
Google Scholar

[24]

A. Kufner, O. John and S. Fučík,
Function Spaces,
Noordhoff International, Leyden, 1977.
Google Scholar

[25]

O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva,
Linear and Quasilinear Equations of Parabolic Type,
Transl. Math. Monogr. 23,
American Mathematical Society, Providence, 1968.
Google Scholar

[26]

K. A. Lurye,
Optimal Control in Problems of Mathematical Physics,
“Nauka”, Moscow, 1975.
Google Scholar

[27]

M. Niezgódka,
Control of parabolic systems with free boundaries—Application of inverse formulations,
Control Cybernet. 8 (1979), no. 3, 213–225.
Google Scholar

[28]

S. M. Nikol’skii,
Approximation of Functions of Several Variables and Imbedding Theorems,
Springer, Heidelberg, 1975.
Google Scholar

[29]

R. H. Nochetto and C. Verdi,
The combined use of a nonlinear Chernoff formula with a regularization procedure for two-phase Stefan problems,
Numer. Funct. Anal. Optim. 9 (1987/88), no. 11–12, 1177–1192.
Google Scholar

[30]

M. Primicerio,
The Occurence of pathologies in some Stefan-like problems,
Numerical Treatment of Free Boundary-Value Problems,
Internat. Ser. Numer. Math. 58,
Birkhäuser, Basel (1982), 233–244.
Google Scholar

[31]

C. Sagues,
Simulation and optimal control of free boundary,
Numerical Treatment of Free Boundary-Value Problems,
Internat. Ser. Numer. Math. 58,
Birkhäuser, Basel (1982), 270–287.
Google Scholar

[32]

B. Sherman,
General one-phase Stefan problems and free boundary problems for the heat equation with Cauchy data prescribed on the free boundary,
SIAM J. Appl. Math. 20 (1971), 555–570.
CrossrefGoogle Scholar

[33]

V. A. Solonnikov,
A priori estimates for solutions of second-order equations of parabolic type,
Tr. Mat. Inst. Steklova 70 (1964), 133–212.
Google Scholar

[34]

V. A. Solonnikov,
On boundary value problems for linear parabolic systems of differential equations of general form,
Tr. Mat. Inst. Steklova 83 (1965), 3–163.
Google Scholar

[35]

G. Talenti and S. Vessella,
A note on an ill-posed problem for the heat equation,
J. Austral. Math. Soc. Ser. A 32 (1982), no. 3, 358–368.
CrossrefGoogle Scholar

[36]

F. P. Vasil’ev,
The existence of a solution to a certain optimal Stefan problem (in Russian),
Comput. Meth. Programm. 12 (1969), 110–114.
Google Scholar

[37]

K. Yosida,
Functional Analysis, Reprint of the 6th ed.,
Classics Math.,
Springer, Berlin, 1995.
Google Scholar

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