Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] W. Fulks and J. S. Maybee, A singular nonlinear equation, Osaka Math. J. 12(1960), 1-19 MR 0123095
  • [2] C. A. Stuart, Existence theorems for a class of nonlinear integral equations, Math. Z. 137 (1974), 49-66 MR 0348416
  • [3] C. A. Stuart, Existence and approximation of solutions of nonlinear elliptic equations, Math. Z. 147 (1976), 53-63 MR 0404854
  • [4] M. G. Crandall, P. H. Rabinowitz, and L. Tartar, On a Dirichlet problem with a singular nonlinearity, TSR 1680, University of Wisconsin, 1976 MR 0427826
  • [5] 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
  • [6] 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
  • [7] 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 MR 556792
  • [8] 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
  • [9] 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 MR 542697
  • [10] J. E. Bouillet and C. Atkinson, A generalized diffusion equation: Radial symmetries and comparison theorems, J. Math. Anal. Appl. (to appear)
  • [11] J. E. Bouillet, Heat-flux comparison based on properties of the medium, Adv. Appl. Math. (1981), 76-90 MR 612513
  • [12] F. V. Atkinson, and L. A. Peletier, Similarity solutions of the nonlinear diffusion equation, Arch. Rat. Mech. Anal. 54(1974), 374-392 MR 0344559
  • [13] 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
  • [14] 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
  • [15] 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

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 35K55, 80A20

Retrieve articles in all journals with MSC: 35K55, 80A20

Additional Information

DOI: https://doi.org/10.1090/qam/766876
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society