On some doubly-nonlinear parabolic equations posed in $ \mathbb{R}^{{d}} $

Goro Akagi

doi:10.3934/dcdss.2023153

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2023, Volume 16, Issue 12: 3661-3676. Doi: 10.3934/dcdss.2023153

This issue Previous Article The anisotropic Cahn–Hilliard equation: Regularity theory and strict separation properties Next Article Degenerate diffusion with Preisach hysteresis

On some doubly-nonlinear parabolic equations posed in $ \mathbb{R}^{{d}} $

Goro Akagi^,

Tohoku University, Japan

^*Corresponding author: Goro Akagi
^*Corresponding author: Goro Akagi

Dedicated to Professor Pierluigi Colli on the occasion of his 65th birthday

Received: July 2023

Revised: August 2023

Early access: August 2023

Published: December 2023

The author is supported by JSPS KAKENHI Grant Numbers JP21KK0044, JP21K18581, JP20H01812 and JP20H00117. This work was supported by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.

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Abstract

In this manuscript, existence of strong solutions to the Cauchy problem for a doubly-nonlinear parabolic equation posed in $ \mathbb{R}^d $ is proved based on Colli's result [16], which extends the celebrated Colli-Visintin theory to Banach space settings, as well as the localized Minty's trick, which can also cover a wide class of PDEs in unbounded domains and enable us to overcome difficulties in identification of weak limits arising from the lack of compact embeddings due to the unboundedness of domains.

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Mathematics Subject Classification: Primary: 35K61; Secondary: 47J35.

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References

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