ON EXISTENCE AND UNIQUENESS IN A FREE BOUNDARY PROBLEM FROM COMBUSTION

REFERENCES

• Caffarelli , L.A. and Vazquez , J.L. 1995 . A Free-Boundary Problem for the Heat Equation Arising in Flame Propagation . Trans. Amer. Math. Soc. , 347 ( 2 ) : 411 – 441 .
   Web of Science ®Google Scholar
• Vazquez , J.L. 1996 . “ The Free Boundary Problem for the Heat Equation with Fixed Gradient Condition ” . In Free Boundary Problems, Theory and Applications (Zakopane, 1995) , Pitman Res. Notes Math. Ser. 363 277 – 302 . Harlow : Longman .
   Google Scholar
• Caffarelli , L.A , Lederman , C. and Wolanski , N. 1997 . Uniform Estimates and Limits for a Two Phase Parabolic Singular Perturbation Problem . Indiana Univ. Math. J. , 46 ( 2 ) : 453 – 489 .
   Web of Science ®Google Scholar
• Caffarelli , L.A. , Lederman , C. and Wolanski , N. 1997 . Pointwise and Viscosity Solutions for the Limit of a Two Phase Parabolic Singular Perturbation Problem . Indiana Univ. Math. J. , 46 ( 3 ) : 719 – 740 .
   Web of Science ®Google Scholar
• Lederman , C. , Vazquez , J.L. and Wolanski , N. 2001 . Uniqueness of Solution to a Free Boundary Problem from Combustion . Trans. Amer. Math. Soc. , 353 ( 2 ) : 655 – 692 .
   Google Scholar
• Galaktionov , V.A. , Hulshof , J. and Vazquez , J.L. 1997 . Extinction and Focusing Behaviour of Spherical and Annular Flames Described by a Free Boundary Problem . J. Math. Pures Appl. (9) , 76 ( 7 ) : 563 – 608 .
   Google Scholar
• Meǐrmanov , A.M. 1981 . On a Problem with a Free Boundary for Parabolic Equations . Mat. Sb. (N.S.) , 115 (157) : 532 – 543 . (In Russian.), (4)
   Google Scholar
• Andreucci , D. and Gianni , R. 1994 . Classical Solutions to a Multidimensional Free Boundary Problem Arising in Combustion Theory . Comm. Partial Differential Equations , 19 ( 5–6 ) : 803 – 826 .
   Web of Science ®Google Scholar
• Petrosyan , A. Convexity and Uniqueness in a Free Boundary Problem Arising in Combustion Theory . To appear in Rev. Mat. Iberoamericana. ,
   Google Scholar
• Henrot , A. and Shahgholian , H. Existence of Classical Solutions to a Free Boundary Problem for the p-Laplace Operator: (I) The Exterior Convex Case . To appear in J. Reine Angew. Math. ,
   Google Scholar
• Henrot , A. and Shahgholian , H. Existence of Classical Solutions to a Free Boundary Problem for the p-Laplace Operator: (II) The Interior Convex Case . To appear in Indiana Univ. Math. J. ,
   Google Scholar
• Daskalopoulos , P. and Lee , K. All the Time Existence of a Smooth Solution for the One-phase Free Boundary Problem of the Flame Type . Preprint
   Google Scholar
• Beurling , A. 1958 . On Free-boundary Problems for the Laplace Equation . Sem. Analytic Functions , 1 : 248 – 263 .
   Google Scholar
• Athanasopoulos , I. , Caffarelli , L. and Salsa , S. 1996 . Caloric Functions in Lipschitz Domains and the Regularity of Solutions to Phase Transition Problems . Annals of Math. , 143 : 413 – 434 .
   Web of Science ®Google Scholar
• Korevaar , N. 1983 . Convex Solutions to Nonlinear Elliptic and Parabolic Boundary Value Problems . Indiana Univ. Math. J. , 32 ( 4 ) : 603 – 614 .
   Web of Science ®Google Scholar
• Brascamp , H.J. and Lieb , E.H. 1976 . On Extensions of the Brunn-Minkowski and Prékopa-Leindler Theorems, Including Inequalities for Log Concave Functions, and with an Application to the Diffusion Equation . J. Functional Analysis , 22 ( 4 ) : 366 – 389 .
   Web of Science ®Google Scholar
• Lieberman , G.M. 1996 . Second Order Parabolic Differential Equations River Edge, NJ : World Scientific Publishing Co., Inc. .
   Google Scholar
• Kinderlehrer , D. and Nirenberg , L. 1977 . Regularity in Free Boundary Problems . Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , 4 ( 2 ) : 373 – 391 .
   Google Scholar