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<p>In this article, we study a reaction–diffusion system with <i>m</i> unknown concentrations where the nonlinearities arise from an underlying reversible chemical reaction. Our objective is to address the existence of global in time solutions for the degenerate systems, i.e., when one or more species stops diffusing. In this regard, we show that a weak global in time solutions exists for all the degenerate cases in any spatial dimension. We are further able to show that classical global in time solutions exists for all the degenerate cases (except one) in any spatial dimension and classical global in time solution exists even for that exceptional case up to spatial dimension 2. We also address the existence of global in time classical solutions to this exceptional case under various growth assumptions on the nonlinearities.</p>

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Existence of solution of a triangular degenerate reaction–diffusion system

  • 期刊论文

  • 发表日期：

    2025年5月24日

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  • Saumyajit Das

摘要

In this article, we study a reaction–diffusion system with m unknown concentrations where the nonlinearities arise from an underlying reversible chemical reaction. Our objective is to address the existence of global in time solutions for the degenerate systems, i.e., when one or more species stops diffusing. In this regard, we show that a weak global in time solutions exists for all the degenerate cases in any spatial dimension. We are further able to show that classical global in time solutions exists for all the degenerate cases (except one) in any spatial dimension and classical global in time solution exists even for that exceptional case up to spatial dimension 2. We also address the existence of global in time classical solutions to this exceptional case under various growth assumptions on the nonlinearities.