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We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces.
Galina I. Bizhanova. "On the Stefan problem with a small parameter." Banach Center Publications 81.1 (2008): 43-63. <http://eudml.org/doc/281622>.
@article{GalinaI2008, abstract = {We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces.}, author = {Galina I. Bizhanova}, journal = {Banach Center Publications}, keywords = {free boundary problem; parabolic equation; small parameter; Hölder space; existence; estimate of solution; Stefan problem; Florin problem}, language = {eng}, number = {1}, pages = {43-63}, title = {On the Stefan problem with a small parameter}, url = {http://eudml.org/doc/281622}, volume = {81}, year = {2008}, }
TY - JOUR AU - Galina I. Bizhanova TI - On the Stefan problem with a small parameter JO - Banach Center Publications PY - 2008 VL - 81 IS - 1 SP - 43 EP - 63 AB - We consider the multidimensional two-phase Stefan problem with a small parameter κ in the Stefan condition, due to which the problem becomes singularly perturbed. We prove unique solvability and a coercive uniform (with respect to κ) estimate of the solution of the Stefan problem for t ≤ T₀, T₀ independent of κ, and the existence and estimate of the solution of the Florin problem (Stefan problem with κ = 0) in Hölder spaces. LA - eng KW - free boundary problem; parabolic equation; small parameter; Hölder space; existence; estimate of solution; Stefan problem; Florin problem UR - http://eudml.org/doc/281622 ER -