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<p>The primary objective of this paper is to investigate an abstract differential system comprising an evolution equation with history-dependent operator and a doubly nonlinear inclusion with nonmonotone perturbation. The latter arises from enthalpy formulation of heat conduction problems involving phase change and nonmonotone source. We firstly introduce a hybrid iterative system by using the implicit time discretization method, pseudomonotone operators theory and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limit procedure for solutions of the hybrid iterative system, we show the existence of solutions to the original problem. Finally, an example of two-phase Stefan problem governed by a diffusion process is provided.</p>

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Existence of Solutions for a Differential System Involving Doubly Nonlinear Inclusions

  • 期刊论文

  • 发表日期：

    2025年2月4日

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  • Jing Zhao,
  • Zijia Peng,
  • Zhenhai Liu

摘要

The primary objective of this paper is to investigate an abstract differential system comprising an evolution equation with history-dependent operator and a doubly nonlinear inclusion with nonmonotone perturbation. The latter arises from enthalpy formulation of heat conduction problems involving phase change and nonmonotone source. We firstly introduce a hybrid iterative system by using the implicit time discretization method, pseudomonotone operators theory and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limit procedure for solutions of the hybrid iterative system, we show the existence of solutions to the original problem. Finally, an example of two-phase Stefan problem governed by a diffusion process is provided.