Author | Antontsev, S. N. author |
---|---|
Title | Energy Methods for Free Boundary Problems [electronic resource] : Applications to Nonlinear PDEs and Fluid Mechanics / by S. N. Antontsev, J. I. Dรญaz, S. Shmarev |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-0091-8 |
Descript | XI, 332 p. online resource |
1 Localized Solutions of Nonlinear Stationary Problems -- 1 Introduction -- 2 Second-order elliptic equations -- 3 The weighted diffusion/absorption balance -- 4 Anisotropic equations: Diffusion/absorption balance -- 5 Systems of second-order elliptic equations -- 6 Higher-order elliptic equations -- 7 Bibliographical notes and open problems -- 2 Stabilization in a Finite Time to a Stationary State -- 1 Introduction -- 2. Second-order parabolic equations -- 3 The weighted diffusion-absorption balance -- 4 The Cauchy problem -- 5 Equations with nonpower and isotropic nonlinearities -- 6 Systems of equations of combined type -- 7 Higher-order parabolic equations and other applications -- 8 Bibliographical notes and open problems -- 3 Space and Time Localization in Nonlinear Evolution Problems -- 1 Introduction -- 2 General second-order equations -- 3 The waiting time property -- 4 Shrinking of supports and formation of a dead core -- 5 Equations with nonhomogeneous absorption terms -- 6 Equations with anisotropic nonlinearities -- 7 Systems of parabolic equations -- 8 Higher-order parabolic equations -- 9 Bibliographical notes -- 4 Applications to Problems in Fluid Mechanics -- 1 Introduction -- 2 The balance laws of fluid mechanics -- 3 Stationary problems of gas dynamics with free boundaries -- 4 Two-phase filtration of immiscible incompressible fluids -- 5 Flows of gas with density-dependent viscosity -- 6 Viscous-elastic media -- 7 Flows of nonhomogeneous non-Newtonian fluid -- 8 Boundary layers in dilatant fluid -- 9 Boussinesq system involving nonlinear thermal diffusion -- 10 Simultaneous motion in the surface channel and the underground water -- 11 Solute transport through a porous medium with micro and macro structures -- 12 A quasilinear degenerate system arising in semiconductor theory -- 13 Blowup in solutions of the thermistor problem -- The function spaces -- Elementary inequalities -- 2.1 Algebraic inequalities -- 2.2 Integral inequalities -- 3 Embedding theorems -- 3.1 Interpolation inequalities -- 3.2 Anisotropic function spaces -- References