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<p>In this work, a nonlinear parabolic-type differential equation with an arbitrary power nonlinearity is considered. A theorem on the existence and uniqueness of the solution of the given equation in the domain of analyticity is formulated and proven. The solution is sought in the form of a power series, accompanied by the determination of the convergence region of this series in the vicinity of the initial conditions. An error estimate for the series is obtained, along with the error arising from analytical continuation. Based on the obtained results, a numerical experiment was conducted.</p>

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An analytical approximate solution of a parabolic-type equation with power nonlinearity in the domain of analyticity

  • 期刊论文

  • 发表日期：

    2026年2月16日

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  • Magomedyusuf Gasanov

摘要

In this work, a nonlinear parabolic-type differential equation with an arbitrary power nonlinearity is considered. A theorem on the existence and uniqueness of the solution of the given equation in the domain of analyticity is formulated and proven. The solution is sought in the form of a power series, accompanied by the determination of the convergence region of this series in the vicinity of the initial conditions. An error estimate for the series is obtained, along with the error arising from analytical continuation. Based on the obtained results, a numerical experiment was conducted.