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The Cauchy Problem for a Doubly Nonlinear Parabolic Equation with Variable Density and Nonlinear Time-Dependent Absorption

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Based on a self-similar analysis of the Fujita type global solvability, we obtain estimates for a solution and fronts (a free boundary) of the Cauchy problem for a doubly nonlinear nondivergence-form parabolic equation with variable density. We consider the case where the absorpiton depends on time and study the asymptotic behavior of the finite self-similar solution depending on numerical parameters characterizing a nonlinear medium. The main results are illustrated by numerical examples.

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Authors and Affiliations

  1. Mirzo Ulugbek National University of Uzbekistan, 4, University St., 100174, Tashkent, Uzbekistan

    Mersaid Aripov & Makhmud Bobokandov

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  1. Mersaid Aripov
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  2. Makhmud Bobokandov
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Correspondence to Mersaid Aripov.

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Aripov, M., Bobokandov, M. The Cauchy Problem for a Doubly Nonlinear Parabolic Equation with Variable Density and Nonlinear Time-Dependent Absorption. J Math Sci 277, 355–365 (2023). https://doi.org/10.1007/s10958-023-06840-0

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  • DOI: https://doi.org/10.1007/s10958-023-06840-0

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