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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Xu, Si and Song, Zifen 2011. Critical parameter equations for degenerate parabolic equations coupled via nonlinear boundary flux. Boundary Value Problems, Vol. 2011, Issue. 1, p. 15.

    Bogoya, Mauricio 2010. Blowing up boundary conditions for a nonlocal nonlinear diffusion equation in several space dimensions. Nonlinear Analysis: Theory, Methods & Applications, Vol. 72, Issue. 1, p. 143.

    Bogoya, M. Ferreira, R. and Rossi, J.D. 2008. A nonlocal nonlinear diffusion equation with blowing up boundary conditions. Journal of Mathematical Analysis and Applications, Vol. 337, Issue. 2, p. 1284.

  • European Journal of Applied Mathematics, Volume 2, Issue 2
  • June 1991, pp. 159-169

Diffusivity determination in nonlinear diffusion

  • Carmen Cortázar (a1), Manuel Elgueta (a1) and Juan Luis Vázquez (a2)
  • DOI:
  • Published online: 01 July 2009

We are concerned with the problem of determining the diffusivity D of a diffusion process governed by the equation ut = (Dux)x', under the assumption that D depends on u. The main point consists in the observation that there exist solutions of travelling-wave type and that the dependence D = D(u) can be explicitly found in terms of the profile of such solutions. The property of finite propagation speed is required for this method to work. We propose two concrete implementations of the inverse problem, and give a rigorous mathematical proof of our statements. We also describe the application of the travelling-wave method to another interesting class of nonlinear parabolic equations.

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D. G. Aronson 1986 The porous medium equation, in: A. Fasano & M. Primicerio , eds., Nonlinear Diffusion Problems. Lecture Notes in Mathematics, Vol. 1224, Springer-Verlag.

C. Bardos , F. Golse , B. Perthame & R. Sentis 1988 The nonaccretive radiative transfer equation: existence of solutions and Rosseland approximation. J. Fund. Anal. 77, 434460.

J. R. Esteban & J. L. Vazquen 1988 Homogeneous diffusion in R with power-like non-linear diffusivity. Arch. Rat. Mech. Anal. 103, 3980.

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B. H. Gilding & L. A. Peletier 1977 On a class of similarity solutions of the porous media equation II. J. Math. Anal. Appl. 57, 552–538.

M. Gurtin & R. C. MacCamy 1977 On the diffusion of biological populations. Math. Biosciences 33, 3549.

A. Lorenzi 1985 An inverse problem for a quasilinear parabolic equation. Ann. Mat. Pura. Appl. 142, 145169.

E. W. Larsen & G. C. Pomraning 1980 Asymptotic analysis of nonlinear Marshak waves. SIAM J. Appl. Math. 39, 201212.

B. Mercier 1987 Application of accetive operators to the radiative transfer equation. SIAM J. Math. Anal. 18, 393408.

L. A. Peletier 1974 A necessary and sufficient condition for the existence of an interface in flows through porous media. Arch. Rat. Mech. Anal. 56, 183190.

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European Journal of Applied Mathematics
  • ISSN: 0956-7925
  • EISSN: 1469-4425
  • URL: /core/journals/european-journal-of-applied-mathematics
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