Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder’s estimates for a degenerate parabolic problem with dynamic boundary conditions

被引：0
作者：
S. P. Degtyarev
机构：
[1] Institute of Applied Mathematics and Mechanics NASU,
来源：
Nonlinear Differential Equations and Applications NoDEA | 2015年 / 22卷
关键词：
Primary 35R35; Secondary 35K65; 35R37; 35K60; Free boundary; Stefan problem; Classical solvability; Porous medium equation; Degenerate parabolic equations; Dynamic boundary conditions; Schauder estimates;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We consider multidimensional two-phase Stefan problem for degenerate parabolic equations of the porous medium type in classes of smooth functions. First we find a natural Hölder class for the Dirichlet boundary conditions in the initial boundary boundary problem for a degenerate parabolic equation of second order. This class then is used to obtain the Schauder estimates for a degenerate parabolic equation with dynamic boundary conditions. As a result we prove the existence locally in time of a smooth solution for Stefan problem for degenerate parabolic equations.
引用
收藏
页码：185 / 237
页数：52
相关论文
共 87 条
  • [1] Meirmanov A.M.(1981)On the classical solution of the multidimensional Stefan problem for quasilinear parabolic equations Math. USSR Sb. 40 157-178
  • [2] Hanzawa E.-I.(1981)Classical solutions of the Stefan problem Tohoku Math. J. 33 297-335
  • [3] Bazalii B.V.(1988)On classical solvability of the multidimensional Stefan problem for convective motion of a viscous incompressible fluid Math. USSR Sb. 60 1-17
  • [4] Degtyarev S.P.(1991)On conditions for the existence of a classical solution of the Stefan contact problem Math USSR Sb. 69 497-525
  • [5] Radkevich E.V.(1999)Existence of the global classical solution for a two-phase Stefan problem SIAM J. Math. Anal. 30 1264-1281
  • [6] Borodin M.A.(2001)On problems with free boundaries for second-order parabolic equations St. Petersburg Math. J. 12 949-981
  • [7] Bizhanova G.I.(1999)On the classical solvability of the stefan problem in a viscous incompressible fluid flow SIAM J. Math. Anal. 30 584-602
  • [8] Solonnikov V.A.(2002)Two-phase stefan problem as the limit case of two-phase Stefan problem with kinetic condition J. Differ. Equ. 183 189-207
  • [9] Kusaka Y.(2005)All time smooth solutions of the one-phase Stefan problem and the Hele-Shaw flow Commun. Partial Differ. Equ. 29 71-89
  • [10] Tani A.(2001)A Stefan problem for a protocell model with symmetry-breaking bifurcations of analitic solutions Interfaces Free Bound 3 143-199
123456789