## A free boundary focusing problem

HTML articles powered by AMS MathViewer

- by Danielle Hilhorst and Josephus Hulshof PDF
- Proc. Amer. Math. Soc.
**121**(1994), 1193-1202 Request permission

## Abstract:

We consider a one-dimensional free boundary problem arising in combustion theory and establish that all solutions are asymptotically equal to a similarity solution which vanishes in a finite time.## References

- H. Berestycki, L. A. Caffarelli, and L. Nirenberg,
*Uniform estimates for regularization of free boundary problems*, Analysis and partial differential equations, Lecture Notes in Pure and Appl. Math., vol. 122, Dekker, New York, 1990, pp. 567–619. MR**1044809** - M. Bertsch and J. Hulshof,
*Regularity results for an elliptic-parabolic free boundary problem*, Trans. Amer. Math. Soc.**297**(1986), no. 1, 337–350. MR**849483**, DOI 10.1090/S0002-9947-1986-0849483-0 - J. D. Buckmaster and G. S. S. Ludford,
*Theory of laminar flames*, Electronic & Electrical Engineering Research Studies: Pattern Recognition & Image Processing Series, vol. 2, Cambridge University Press, Cambridge-New York, 1982. MR**666866**
L. A. Caffarelli and J. L. Vazquez, - C. M. Dafermos,
*Asymptotic behavior of solutions of evolution equations*, Nonlinear evolution equations (Proc. Sympos., Univ. Wisconsin, Madison, Wis., 1977) Publ. Math. Res. Center Univ. Wisconsin, vol. 40, Academic Press, New York-London, 1978, pp. 103–123. MR**513814** - Roberto Gianni and Josephus Hulshof,
*The semilinear heat equation with a Heaviside source term*, European J. Appl. Math.**3**(1992), no. 4, 367–379. MR**1196817**, DOI 10.1017/S0956792500000917 - Victor Guillemin and Alan Pollack,
*Differential topology*, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1974. MR**0348781** - D. Hilhorst and J. Hulshof,
*An elliptic-parabolic problem in combustion theory: convergence to travelling waves*, Nonlinear Anal.**17**(1991), no. 6, 519–546. MR**1124123**, DOI 10.1016/0362-546X(91)90062-6 - J. Hulshof,
*An elliptic-parabolic free boundary problem: continuity of the interface*, Proc. Roy. Soc. Edinburgh Sect. A**106**(1987), no. 3-4, 327–339. MR**906216**, DOI 10.1017/S030821050001845X - Hiroshi Matano,
*Nonincrease of the lap-number of a solution for a one-dimensional semilinear parabolic equation*, J. Fac. Sci. Univ. Tokyo Sect. IA Math.**29**(1982), no. 2, 401–441. MR**672070**

*A free boundary problem for the heat equation arising in flame propagation*, preprint. E. A. Coddington and N. Levinson,

*Theory of ordinary equations*, Tata McGraw-Hill, New York, 1972.

## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**121**(1994), 1193-1202 - MSC: Primary 35R35; Secondary 35B40, 35K55
- DOI: https://doi.org/10.1090/S0002-9939-1994-1233975-9
- MathSciNet review: 1233975