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<p>In this paper, we examine the well-posedness of Cauchy problems for nonstationary partial differential equations with nondistinguished highest time derivatives that have degeneration by these derivatives. For this purpose, we introduce the notion of the trace on the hyperplane of initial data for distributions with semi-bounded supports, which allows one to establish some properties of the solution that ensure the well-posedness of the problems considered.</p>

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On the Well-Posedness of Cauchy Problems for Nonstationary Equations with the Nondistinguished Highest Time Derivative and the Definition of the Trace of Distribution on the Hyperplane of the Initial Data

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  • 发表日期：

    2025年3月1日

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  • Yu. V. Zasorin

摘要

In this paper, we examine the well-posedness of Cauchy problems for nonstationary partial differential equations with nondistinguished highest time derivatives that have degeneration by these derivatives. For this purpose, we introduce the notion of the trace on the hyperplane of initial data for distributions with semi-bounded supports, which allows one to establish some properties of the solution that ensure the well-posedness of the problems considered.