A nonlinear integral equation occurring in a singular free boundary problem

Authors:
Klaus Höllig and John A. Nohel

Journal:
Trans. Amer. Math. Soc. **283** (1984), 145-155

MSC:
Primary 35R35; Secondary 35K55, 45G10

DOI:
https://doi.org/10.1090/S0002-9947-1984-0735412-5

MathSciNet review:
735412

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the Cauchy problem

**[1]**P. Benilan, M. G. Crandall and A. Pazy, -*accretive operators*(in preparation).**[2]**L. C. Evans,*Application of nonlinear semigroup theory to certain partial differential equations*, Nonlinear Evolution Equations (M. G. Crandall, ed.), Academic Press, New York, 1978. MR**513818 (81b:47078)****[3]**A. Fasano and M. Primicerio,*General free boundary problems for the heat equation*. I, J. Math. Anal. Appl.**57**(1977), 694-723. MR**0487016 (58:6695a)****[4]**-,*General free boundary problems for the heat equation*. II, J. Math. Anal. Appl.**58**(1977), 202-231. MR**0487017 (58:6695b)****[5]**K. Höllig,*Existence of infinitely many solutions for a forward backward heat equation*, Trans. Amer. Math. Soc.**278**(1983), 299-316. MR**697076 (84m:35062)****[6]**K. Höllig and J. A. Nohel,*A diffusion equation with a nonmonotone constitutive function*, Systems of Partial Differential Equations (J. M. Ball, ed.), Reidel, Dordrecht, 1983, pp. 409-422.**[7]**D. Kinderlehrer and L. Nirenberg,*Regularity in free boundary problems*, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4)**4**(1977), 373-391. MR**0440187 (55:13066)****[8]**D. Schaeffer,*A new proof of the infinite differentiability of the free boundary in the Stefan problem*, J. Differential Equations**20**(1976), 266-269. MR**0390499 (52:11325)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0735412-5

Keywords:
Cauchy problem,
parabolic,
nonlinear,
free boundary regularity,
nonlinear singular integral equation

Article copyright:
© Copyright 1984
American Mathematical Society