Asymptotic behavior of temperature in a nonlinear radiating, linear absorbing rod of finite length

Author:
C. V. Pao

Journal:
Quart. Appl. Math. **34** (1977), 429-435

MSC:
Primary 80.35

DOI:
https://doi.org/10.1090/qam/462243

MathSciNet review:
462243

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References | Similar Articles | Additional Information

**[1]**C. Y. Chan,*Positive solutions for nonlinear parabolic second initial boundary-value problem*, Quart. Appl. Math.**31**, 443-454 (1974) MR**0427832****[2]**A. Friedman,*Generalized heat transfer between solids and gases under nonlinear boundary conditions*, J. Math. Mech.**8**, 161-183 (1959) MR**0102345****[3]**R. A. Handelsman and W. E. Olmstead,*Asymptotic solution to a class of nonlinear Volterra integral equations*, SIAM J. Appl. Math.**22**, 373-384 (1972) MR**0310574****[4]**J. E. Hartka,*Temperature of a semi-infinite rod which radiates both linearly and nonlinearly*, Quart. Appl. Math.**32**, 101-111 (1974) MR**0430539****[5]**J. B. Keller and W. E. Olmstead,*Temperature of a nonlinearly radiating semi-linear solid*, Quart. Appl. Math.**29**, 559-566 (1972) MR**0403430****[6]**H. A. Levine and L. E. Payne,*Non-existence theorem for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time*, J. Diff. Eqns.**16**, 319-334 (1974) MR**0470481****[7]**W. R. Mann and F. Wolf,*Heat transfer between solids and gases under nonlinear boundary conditions*, Quart. Appl. Math.**9**, 163-184 (1951) MR**0042596****[8]**K. Padmavally,*On a nonlinear integral equation*, J. Math. Mech.**7**, 533-555 (1958) MR**0103400****[9]**C. V. Pao,*Successive approximations of some nonlinear initial boundary-value problems*, SIAM J. Math. Anal.**5**, 91-102 (1974) MR**0339507****[10]**C. V. Pao,*Positive solutions of a nonlinear boundary-value problem of parabolic type*, J. Diff. Eqns.**22**, 145-163 (1976) MR**0422876****[11]**M. H. Protter and H. F. Weinberger,*Maximum principles in differential equations*, Prentice-Hall, Englewood Cliffs, 1967 MR**0219861**

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DOI:
https://doi.org/10.1090/qam/462243

Article copyright:
© Copyright 1977
American Mathematical Society