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Evolution equations and subdifferentials in Banach spaces
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Principle of symmetric criticality and evolution equations
1.  Department of Applied Physics, School of Science and Engineering, Waseda University, 341 Ohkubo, Shinjukuku, Tokyo 1698555, Japan 
2.  Department of Applied Physics, School of Science and Engineering, Waseda University, 341, Okubo, Tokyo, 1698555 
The purpose of this paper is to combine this result with the abstract theory developed in [1] and [2] concerning the evolution equation: $du(t)$/$dt + \partial\upsilon^1(u(t)) \partial\upsilon^2(u(t))$ ∋ $f(t)$ in V*, where $\partial\upsilon^i$ is the socalled subdifferential operator from a Banach space X into its dual V*. It is assumed that there exists a Hilbert space H satisfying $V \subset H \subset V $ and that G acts on these spaces as isometries. In this setting, the existence of Gsymmetric solution for above equation can be discussed.
As an application, a parabolic problem with the pLaplacian in unbounded domains is discussed.
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