Abstract
Nonlocal transformations of some quasilinear parabolic equations which describe spherically symmetric heat conduction and diffusion processes are considered. One of them transforms the equationr n−1θ t =(r n−1|θ r |lθ r ) r to an equation of the same type but with a different value of the exponent n. Another transformation reduces the equationr n−1θ t =(r n−1θ−2θ r ) r to an equation with coefficients which do not depend on the space variable. The third nonlocal transformation preserves the equationrθ t =(rθ −1θ r ) r . Some exact solutions of the mentioned equations are analyzed. Bibliography: 15 titles.
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Additional information
Dedicated to V. A. Solonnikov on his sixtieth anniversary
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 213, 1994, pp. 151–163.
Translated by S. Yu. Pilyugin
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Pukhnachov, V.V. Reciprocity transformations for radial nonlinear heat equations. J Math Sci 84, 911–918 (1997). https://doi.org/10.1007/BF02399942
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DOI: https://doi.org/10.1007/BF02399942