Abstract
We consider the questions of existence, uniqueness and interface behaviour for nonnegative solutions of the Cauchy Problem where u 0 is a continuous and nonnegative function which can be unbounded on R, in the exponent range 1 <p<m.
Supported by grant No. 06-0361-0682 from the United States-Israel BSF.
Supported by EEC Contract SC1-0019-C(TT).
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References
D. G. Aronson, The Porous Medium Equation, in Nonlinear Diffusion Problems, Lecture Notes in Maths. 1224. C.I.M.E. Series, Springer Verlag, Berlin, 1986..
M. Bertsch, R. Kersner, L. A. Peletier, Positivity versus localization in degenerate diffusion equations, Nonlin. Anal. TMA 9 (1985), 987–10098.
M. Bertsch, T. Nanbu, L. A. Peletier, Decay of solutions of a degenerate nonlinear diffusion equation, Nonlin. Anal. TMA 6 (1982), 539–554.
B. E. J. Dahlberg, C. E. Kenig, Non-negative solutions of the porous medium equation, Comm. P. D. E. 9 (1984), 409–437.
A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, N. J., 1962.
M. A. Herrero, J. L. Vazquez, Thermal waves in absorbing media, J. Diff. Eq. 74 2 (1988), 218–233.
A. S. Kalashnikov, The effect of absorption of heat propagation in a medium in which thermal conductivity depends on temperature, Zh. vy-chisl. math, i math. phys. 16 (1976).
R. Kersner, Degenerate parabolic equations with general nonlinearities, Nonlin. Anal., TMA 4 (1980), 1043–1062.
B. F. Knerr, The porous medium equation in one dimension, Trans. Amer. Math. Soc. 234 (1977), 381–415.
J. B. McLeod, L. A. Peletier, J. L. Vazquez, Solutions of a nonlinear ODE appearing in the theory of diffusion with absorption, Differential and Integral Equations 4 (1991), 1–14.
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© 1992 Springer Science+Business Media New York
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Kamin, S., Peletier, L.A., Vazquez, J.L. (1992). A Nonlinear Diffusion-Absorption Equation with Unbounded Initial Data. In: Lloyd, N.G., Ni, W.M., Peletier, L.A., Serrin, J. (eds) Nonlinear Diffusion Equations and Their Equilibrium States, 3. Progress in Nonlinear Differential Equations and Their Applications, vol 7. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0393-3_18
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DOI: https://doi.org/10.1007/978-1-4612-0393-3_18
Publisher Name: Birkhäuser, Boston, MA
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