The propagation of the free boundary of the solution of the dam problem and related problems

References

• Alt , H. W. 1979 . Strömungen durch inhomogene poröse Medien mit freiem Rand . J. Reine Ang. Math. , 305 : 255 – 272 .
   Google Scholar
• Alt , H. W. 1983 . “ The dam problem ” . In in:Free boundary problems:theory and applications , Edited by: Fasano and Primicerio . Vol. I , 2 – 68 . London : Pitman .
   Google Scholar
• Alt , H. W. , Luckhaus , S . and Visintin , A. 1984 . On nonstationary flow through porous media . Ann. Mat. Pura Appl. , CXXXVI : 303 – 316 .
   Google Scholar
• Alvarez , L. , Díaz , J .I. and Kersner , R. 1988 . “ On the initial growth of the interfaces in nonlinear diffusion-convection processes ” . In in:Nonlinear diffusion equations and their equilibrium states , Edited by: Ni , W.N. , Peletier , L.A. and Serrin , J. Vol. I , 1 – 20 . New York : Springer Verlag .
   Google Scholar
• Fasano and Primicerio , eds. 1986 . “ The porous medium equation ” . In in:Nonlinear diffusion problems , 1 – 46 . Springer Verlag . Lecture Notes in Mathematics no1224
   Google Scholar
• Baiocchi , C. 1972 . Su un problema di frontiera libera connesso a questioni di idraulica . Ann. Mat. Pura Appl. IV , XCII : 107 – 127 .
   Google Scholar
• Baiocchi , C . and Capelo , A. 1983 . “ Variational and Quasivariational Inequalities ” . In Applications to Free Boundary Problems , Chichester : Wiley .
   Google Scholar
• Bayada , G. , Boukrouch , M. and El Talaoui Talibi , M. 1990 . Du problème de Hele-Shaw au problème de la cavitation en lubrification hydrodynamique , Prepublication no100 du Lab. d'Analyse Numerique, Univ. de Lion .
   Google Scholar
• Bear , J. 1989 . Hydraulics of Groundwater , Edited by: Bertsch , M. in:Some Topics in Nonlinear PDE's, proc. Int. Conf. Torino . McGraw-Hill ,New York ,1979
   Google Scholar
• Brezis , H. , Kinderlehrer , D. and Stampacchia , G. 1973 . Sur une nouvelle formulation du problème d'écoulement à travers une digue . C.R. Acad. Sc. , 276 : 129 – 132 .
   Google Scholar
• Caffarelli , L. A. and Friedman , A. 1987 . Asymptotic behaviour of solutions of ut[d] [d]umas t [d] [d] . Indiana Univ. Math. J. , 36 ( 4 ) : 711 – 718 .
   Google Scholar
• Carrillo J. Uniqueness and periodic behaviour of the solution to the evolution dam problem to appear
   Google Scholar
• Carrillo , J. and Chipot , M. 1982 . On the dam problem . J. Diff. Eqns , 45 ( 4 ) : 234 – 271 .
   Google Scholar
• Carrillo , J. and Gilardi , G. 1990 . La vitesse de propagation dans le problème de la digue . Ann. Faculté des Sciences de Toulouse , 11 ( 4 ) : 7 – 27 .
   Google Scholar
• Crank , J. 1984 . Free and moving boundary problems , Oxford : Clarendon Press .
   Google Scholar
• Díaz , J.I. 1985 . Nonlinear partial differential equations and free boundaries , Vol. 106 , London : I, Elliptic equations, Pitman .
   Google Scholar
• Díaz , J.I. 1986 . Elliptic and parabolic quasilinear equations giving rise to a free boundary , Edited by: Browder , F.E. Vol. 1 , 381 – 393 . the boundary of the support of the solution, in:Nonlinear functional analysis and its applications .
   Google Scholar
• Di Benedetto , E. and Friedman , A. 1986 . Periodic behaviour for the evolutionary dam problem and related free boundary problems . Comm. on Partial Diff. Equations , 11 : 1297 – 1377 .
   Google Scholar
• Di Benedetto , E. and Friedman , A. 1985 . Bubble growth in porous media . Indiana Univ. Math. J. , 16 ( 2 ) : 279 – 300 .
   Google Scholar
• Elliott , C .M. and Ockendon , J.R. 1982 . Weak and variational methods for moving boundary problems , Vol. 59 , Pitman .
   Google Scholar
• Friedman , A. 1982 . Variational Principles and Free Boundary Problems , New York : Wiley .
   Google Scholar
• Gilardi , G. 1979 . A new approach to evolution free boundary problems . Comm. on Partial Diff, Equations , 4 : 1099 – 1123 .
   Google Scholar
• Gilardi , G. 1980 . A new approach to evolution free boundary problems . Comm. on Partial Diff, Equations , 5 : 983 – 984 .
   Google Scholar
• Gilardi G. The speed of propagation in the dam problem proc. I Reunion Hispano-ltaliana de Analisis non Lineal y Matematica Aplicada El Escorial June 1989 5 9
   Google Scholar
• Gilardi G. The support of the solution in the dam problem, in:Free Boundary Problems:Theory and Applications proc. International Colloquium on Free Boundary Problems:Theory and Applications Montreal/Canada June 1990 13 22 to appear
   Google Scholar
• Gilardi G. Kroner D. The dam problem in unbounded domains to appear
   Google Scholar
• Gilardi G. Luckhaus S. A regularity result for the solution of the dam problem to appear
   Google Scholar
• Howison , S. D. 1986 . Bubble growth in porous media and Hele-Shaw cells . Proc. of the Royal Soc Edinb. , 102 A : 141 – 148 .
   Google Scholar
• Kinderlehrer , D. 1980 . An Introduction to Variational Inequalities and Their Applications , New York : Academic Press .
   Google Scholar
• Torelli , A. 1975 . Su un problema di frontiera libera di evoluzione . Boll. U.M.I. , 11 ( 4 ) : 559 – 570 .
   Google Scholar
• Vázquez , J. L. 1987 . “ Hyperbolic aspects in the theory of the porous medium equation ” . In in:Metastability and incompletely posed problems , Edited by: Antman et al . 325 – 342 . Springer Verlag .
   Google Scholar
• Visintin , A. 1980 . Existence results for some free boundary filtration problems . Ann. Mat. Pura Appl. , CXXIV ( IV ) : 293 – 320 .
   Google Scholar