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Abstract <p> We consider multidimensional generalized Monge–Ampère evolution equationswith right-hand sides that, in addition to the determinant of the Hesse matrix, may depend on theLaplace operator and the gradient of the unknown function. A version of the reduction method forconstructing exact multidimensional solutions of the generalized Monge–Ampèreevolution equations using separation of variables is proposed. Multivariate exact solutionsexpressed in closed form via elementary functions and via solutions of ordinary differentialequations are obtained. A number of examples of exact solutions, both radially symmetric andanisotropic in spatial variables, expressed via combinations of elementary functions are given.</p>

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On Multidimensional Exact Solutions of the Generalized Monge–Ampère Evolution Equations

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. A. Kosov,
  • E. I. Semenov

摘要

Abstract

We consider multidimensional generalized Monge–Ampère evolution equationswith right-hand sides that, in addition to the determinant of the Hesse matrix, may depend on theLaplace operator and the gradient of the unknown function. A version of the reduction method forconstructing exact multidimensional solutions of the generalized Monge–Ampèreevolution equations using separation of variables is proposed. Multivariate exact solutionsexpressed in closed form via elementary functions and via solutions of ordinary differentialequations are obtained. A number of examples of exact solutions, both radially symmetric andanisotropic in spatial variables, expressed via combinations of elementary functions are given.