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Abstract <p> The asymptotic behavior of the solution to the Cauchy problem for an inhomogeneous heat equation with a right-hand side that has a self-similar asymptotic behavior at infinity is investigated. Using the auxiliary parameter method and the regularization of singularities of the integrands, we obtain an asymptotic approximation of the solution in the form of an Erdélyi series in half-integer powers of the time variable with coefficients depending on the self-similar variable and the logarithm of time. </p>

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Calculation of the Asymptotics of the Solution of the Inhomogeneous Heat Equation by the Auxiliary Parameter Method

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • S. V. Zakharov

摘要

Abstract

The asymptotic behavior of the solution to the Cauchy problem for an inhomogeneous heat equation with a right-hand side that has a self-similar asymptotic behavior at infinity is investigated. Using the auxiliary parameter method and the regularization of singularities of the integrands, we obtain an asymptotic approximation of the solution in the form of an Erdélyi series in half-integer powers of the time variable with coefficients depending on the self-similar variable and the logarithm of time.