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<p>In this paper, we present new results on the existence of multiple classical solutions to a class of metaparabolic initial-boundary value problems—second-order partial differential equations that generalize classical parabolic equations. We establish sufficient conditions under which these problems admit at least one solution. Our approach leverages a novel fixed-point framework involving the sum of two specialized operators, with the analysis carried out in the context of Morrey spaces. These equations model the dynamics of first-order viscous phase transitions in cooling binary solutions and possess significant theoretical interest. An illustrative example is provided to demonstrate the applicability of the results.</p>

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Multiple classical solutions for a class of metaparabolic initial boundary value problems in Morrey spaces

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Khaled Zennir,
  • Svetlin G. Georgiev,
  • Keltoum Bouhali

摘要

In this paper, we present new results on the existence of multiple classical solutions to a class of metaparabolic initial-boundary value problems—second-order partial differential equations that generalize classical parabolic equations. We establish sufficient conditions under which these problems admit at least one solution. Our approach leverages a novel fixed-point framework involving the sum of two specialized operators, with the analysis carried out in the context of Morrey spaces. These equations model the dynamics of first-order viscous phase transitions in cooling binary solutions and possess significant theoretical interest. An illustrative example is provided to demonstrate the applicability of the results.