VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES

doi:10.1007/s10473-025-0514-y

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (5): 2060-2087.doi: 10.1007/s10473-025-0514-y

VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES

Youssef AHMIDA¹, Ahmed YOUSSFI^2,*

1. Chouaïb Doukkali University, Higher School of Education and Training, Sciences and Technologies Team (ESTE), Road Azzemour, El Jadida, Morocco;
2. Sidi Mohamed Ben Abdellah University, National School of Applied Sciences, Laboratory of Applied Sciences and Innovative Technologies, My Abdellah Avenue, Road Imouzer, P.O. Box 72 Fès-Principale, 30 000, Fez, Morocco

收稿日期:2024-04-23 修回日期:2025-03-21 出版日期:2025-09-25 发布日期:2025-10-14

VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES

Youssef AHMIDA¹, Ahmed YOUSSFI^2,*

1. Chouaïb Doukkali University, Higher School of Education and Training, Sciences and Technologies Team (ESTE), Road Azzemour, El Jadida, Morocco;
2. Sidi Mohamed Ben Abdellah University, National School of Applied Sciences, Laboratory of Applied Sciences and Innovative Technologies, My Abdellah Avenue, Road Imouzer, P.O. Box 72 Fès-Principale, 30 000, Fez, Morocco

Received:2024-04-23 Revised:2025-03-21 Online:2025-09-25 Published:2025-10-14
Contact: ^*Ahmed Youssfi, E-mail: ahmed.youssfi@usmba.ac.ma; ahmed.youssfi@gmail.com
About author:Youssef Ahmida, E-mail: youssef.ahmida@gmail.com

摘要/Abstract

摘要： We consider nonlinear parabolic problems in a variational framework. The leading part is a monotone operator whose growth is controlled by time- and space-dependent Musielak functions. On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions, a Poincaré-type inequality, an integration-by-parts formula and a trace result. Bringing together these results, we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.

关键词: nonlinear parabolic equations, variational solutions, Musielak spaces

Abstract: We consider nonlinear parabolic problems in a variational framework. The leading part is a monotone operator whose growth is controlled by time- and space-dependent Musielak functions. On Musielak's controlling functions we impose regularity conditions which make it possible to extend certain classical results such as the density of smooth functions, a Poincaré-type inequality, an integration-by-parts formula and a trace result. Bringing together these results, we adapt the classical theory of monotone operators and prove the well-posedness of the variational problem.

Key words: nonlinear parabolic equations, variational solutions, Musielak spaces

中图分类号:

35K55

Youssef AHMIDA, Ahmed YOUSSFI. VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES[J]. 数学物理学报(英文版), 2025, 45(5): 2060-2087.

Youssef AHMIDA, Ahmed YOUSSFI. VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES[J]. Acta mathematica scientia,Series B, 2025, 45(5): 2060-2087.

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VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES

VARIATIONAL PARABOLIC PROBLEMS IN MUSIELAK SPACES

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