Solvability of a free-boundary problem for a heterogeneous elastic body
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We consider the free-boundary problem for a stationary elastic system. We prove that the problem has a classical solution if the initial data are close to the stationary solution.
KeywordsFree boundary classical solution elasticity theor.
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- 5.B. V. Bazaliy, “The Stefan problem for the Laplace equation with regard for the curvature of the free boundary,” Ukr. Mat. Zh., 49, No. 10, 1299–1315 (1997).Google Scholar
- 13.O. A. Ladyzhenskaya, V. A. Solonnikov, and N. N. Ural’tseva, Linear and Quasilinear Equations of Parabolic Type, Amer. Math. Soc., Providence, RI, 1968.Google Scholar
- 15.O. A. Oleinik, G. A. Iosif’yan, and A. S. Shamaev, Mathematical Problems of the Theory of Strongly Inhomogeneous Elastic Media [in Russian], MGU, Moscow, 1990.Google Scholar
- 18.Z. G. Sheftel, “Elliptic inequalities and general boundary-value problems for elliptic equations with discontinuous coefficients,” Sib. Mat. Zh., VI, No. 3, 636–668 (1965).Google Scholar
- 19.V. A. Solonnikov, “Estimates of the solution of the second initial boundary-value problem for the Stokes system in the spaces of functions with derivatives continuous by Hölder with respect to spatial variables,” Zapis. POMI, 259, 254–279 (1999).Google Scholar
- 21.V. A. Trenogin, Functional Analysis [in Russian], Nauka, Moscow, 1980.Google Scholar
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