Funkcialaj Ekvacioj
Print ISSN : 0532-8721
Elliptic-Parabolic Quasi-Variational Evolution Equations
Masahiro KuboNoriaki Yamazaki
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JOURNAL OPEN ACCESS

2024 Volume 67 Issue 1 Pages 1-27

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Abstract

We introduce a class of abstract doubly nonlinear evolution equations associated with subdifferential operators depending on the unknown. This is modeled on quasi-variational inequalities for systems of elliptic-parabolic partial differential equations that arise from the flows of multi-component fluids in partially saturated porous media. We prove the existence of a solution by employing the theory of time-dependent subdifferential evolution equations and its generalization. Application examples are given for models of fluid flows and population diffusion with a temperature-dependent constraint.

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© 2024 by the Division of Functional Equations, The Mathematical Society of Japan
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