Geodesic
Classical and weak solutions of the two-phase boundary inverse Stefan problem
Numerical methods and programming, Tome 3 (2002) no. 1, pp. 133-143.

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Two approaches to formulation of the quasilinear two-phase inverse Stefan problem on determining an unknown boundary regime with the Cauchy data on the other boundary of the domain are considered. According to these approaches, the concepts of an exact solution in the Holder classes and a weak exact solution are introduced. Correctness of the statements and uniqueness of solutions are established.
Keywords: Stefan problem, inverse problems, two-phase boundary value problem, boundary regimes, ill-posed problems. 
@article{VMP_2002_3_1_a9,
     author = {N. L. Gol'dman},
     title = {Classical and weak solutions of the two-phase boundary inverse {Stefan} problem},
     journal = {Numerical methods and programming},
     pages = {133--143},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a9/}
}
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N. L. Gol'dman. Classical and weak solutions of the two-phase boundary inverse Stefan problem. Numerical methods and programming, Tome 3 (2002) no. 1, pp. 133-143. http://geodesic.mathdoc.fr/item/VMP_2002_3_1_a9/