An equation with a singular nonlinearity related to diffusion problems in one dimension
Authors:
Julio E. Bouillet and Sônia M. Gomes
Journal:
Quart. Appl. Math. 42 (1985), 395-402
MSC:
Primary 35K55; Secondary 80A20
DOI:
https://doi.org/10.1090/qam/766876
MathSciNet review:
766876
Full-text PDF Free Access
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Additional Information
- W. Fulks and J. S. Maybee, A singular non-linear equation, Osaka Math. J. 12 (1960), 1–19. MR 123095
- C. A. Stuart, Existence theorems for a class of non-linear integral equations, Math. Z. 137 (1974), 49–66. MR 348416, DOI https://doi.org/10.1007/BF01213934
- Charles A. Stuart, Existence and approximation of solutions of non-linear elliptic equations, Math. Z. 147 (1976), no. 1, 53–63. MR 404854, DOI https://doi.org/10.1007/BF01214274
- M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a Dirichlet problem with a singular nonlinearity, Comm. Partial Differential Equations 2 (1977), no. 2, 193–222. MR 427826, DOI https://doi.org/10.1080/03605307708820029
C. Atkinson and C. W. Jones, Similarity solutions in some nonlinear diffusion problems and in boundary-layer flow of a pseudo plastic fluid, Q. J. Mech. Appl. Math. XXVII (1974), 193–211
C. Atkinson, Some asymptotic results for the effect of composition-dependent diffusion on the growth rate of precipitate particles, Q. J. Mech. Appl. Math. XXVII (1974), 299–316
- Julio E. Bouillet, Dolores A. de Saravia, and Luis T. Villa, Similarity solutions of the equation of one-dimensional heat conduction, J. Differential Equations 35 (1980), no. 1, 55–65. MR 556792, DOI https://doi.org/10.1016/0022-0396%2880%2990049-2
D. A. Saravia and J. E. Bouillet, Aproximación lineal por trozos de las soluciones de similaridad de la ecuación de la difusión, con coeficiente dependiente de la concentración, Communication to the 1980 Meeting of the U.M.A., Rev. Un. Mat. Argentina 30, (1981) 55–56
- C. Atkinson and J. E. Bouillet, Some qualitative properties of solutions of a generalised diffusion equation, Math. Proc. Cambridge Philos. Soc. 86 (1979), no. 3, 495–510. MR 542697, DOI https://doi.org/10.1017/S030500410005636X
J. E. Bouillet and C. Atkinson, A generalized diffusion equation: Radial symmetries and comparison theorems, J. Math. Anal. Appl. (to appear)
- Julio E. Bouillet, Heat-flux comparison based on properties of the medium, Adv. in Appl. Math. 2 (1981), no. 1, 76–90. MR 612513, DOI https://doi.org/10.1016/0196-8858%2881%2990039-7
- F. V. Atkinson and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rational Mech. Anal. 54 (1974), 373–392. MR 344559, DOI https://doi.org/10.1007/BF00249197
C. J. van Duyn and L. A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonl. Anal., Theory, Methods Appl. 1 (1977), 223–233
J. E. Bouillet, J. P. Milaszewicz and D. A. Saravia, On approximate similarity solutions of one dimensional diffusion equations, Communication to the SIAM 30th. Anniversary Meeting, July 1982
S. M. Gomes, Existência e comportamento na fronteira de solucão de problema de Dirichelt não linear com singularidade na fronteira. Dissertation, Instituto de Matemática Pura e Aplicada —CNPq—, Rio de Janeiro, December 1982
W. Fulks and J. S. Maybee, A singular nonlinear equation, Osaka Math. J. 12(1960), 1–19
C. A. Stuart, Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974), 49–66
C. A. Stuart, Existence and approximation of solutions of nonlinear elliptic equations, Math. Z. 147 (1976), 53–63
M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a Dirichlet problem with a singular nonlinearity, TSR 1680, University of Wisconsin, 1976
C. Atkinson and C. W. Jones, Similarity solutions in some nonlinear diffusion problems and in boundary-layer flow of a pseudo plastic fluid, Q. J. Mech. Appl. Math. XXVII (1974), 193–211
C. Atkinson, Some asymptotic results for the effect of composition-dependent diffusion on the growth rate of precipitate particles, Q. J. Mech. Appl. Math. XXVII (1974), 299–316
J. E. Bouillet, D. A. Saravia and L. T. Villa, Similarity solutions of the equation of one-dimensional heat conduction, J. Diff. Equations 35 (1980), 55–65
D. A. Saravia and J. E. Bouillet, Aproximación lineal por trozos de las soluciones de similaridad de la ecuación de la difusión, con coeficiente dependiente de la concentración, Communication to the 1980 Meeting of the U.M.A., Rev. Un. Mat. Argentina 30, (1981) 55–56
C. Atkinson and J. E. Bouillet, Some qualitative properties of solutions of a generalised diffusion equation, Math. Proc. Camb. Phil. Soc. 86 (1979), 495–510
J. E. Bouillet and C. Atkinson, A generalized diffusion equation: Radial symmetries and comparison theorems, J. Math. Anal. Appl. (to appear)
J. E. Bouillet, Heat-flux comparison based on properties of the medium, Adv. Appl. Math. (1981), 76–90
F. V. Atkinson, and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rat. Mech. Anal. 54(1974), 374–392
C. J. van Duyn and L. A. Peletier, A class of similarity solutions of the nonlinear diffusion equation, Nonl. Anal., Theory, Methods Appl. 1 (1977), 223–233
J. E. Bouillet, J. P. Milaszewicz and D. A. Saravia, On approximate similarity solutions of one dimensional diffusion equations, Communication to the SIAM 30th. Anniversary Meeting, July 1982
S. M. Gomes, Existência e comportamento na fronteira de solucão de problema de Dirichelt não linear com singularidade na fronteira. Dissertation, Instituto de Matemática Pura e Aplicada —CNPq—, Rio de Janeiro, December 1982
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© Copyright 1985
American Mathematical Society
