Global well-posedness for a time-fractional doubly nonlinear equation

Goro Akagi; Giacomo Enrico Sodini; Ulisse Stefanelli

doi:10.48550/arxiv.2508.13694

August 19, 2025Open Access

Global well-posedness for a time-fractional doubly nonlinear equation

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Key Points

Global weak solutions exist for time-fractional parabolic equations, even with maximal monotone nonlinearities.
The primary method used involves regularization and Galerkin approximation to establish existence and uniqueness.
Maximal monotone graphs are analyzed, showcasing the lack of growth restrictions on nonlinear terms.
Lipschitz continuous perturbations are examined, leading to broader conditions for solution uniqueness.

Implication

This research demonstrates global weak solutions for time-fractional parabolic equations, highlighting uniqueness under specific conditions.

Abstract

We consider a time-fractional parabolic equation of doubly nonlinear type, featuring nonlinear terms both inside and outside the differential operator in time. The main nonlinearities are maximal monotone graphs, without restrictions on the growth. In addition, a Lipschitz continuous perturbation is considered. The existence of global weak solutions is obtained via a regularization and Galerkin approximation method. Uniqueness is also discussed under some additional assumptions.

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Cite This Study

Akagi et al. (2025) studied this question.

synapsesocial.com/papers/68e9b1b5ba7d64b6fc131e59 https://doi.org/10.48550/arxiv.2508.13694

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Global well-posedness for a time-fractional doubly nonlinear equation

Key Points

Implication

Abstract

Discussion

Cite This Study

Global well-posedness for a time-fractional doubly nonlinear equation

Key Points

Implication

Abstract

Discussion

Cite This Study

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