Dept. Math, Hokkaido Univ. EPrints Server

A class of nonlinear evolution equations governed by time-dependent operators of subdifferential type

Preprint Series # 696
Yamazaki, Noriaki A class of nonlinear evolution equations governed by time-dependent operators of subdifferential type. (2005);

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Abstract

Recently there are so many mathematical models which describe nonlinear phenomena. In some phenomena, the free energy functional is not convex. So, the existence-uniqueness question is sometimes difficult. In order to study such phenomena, let us introduce the new class of abstract nonlinear evolution equations governed by time-dependent operators of subdifferential type. In this paper we shall show the existence and uniqueness of solution to nonlinear evolution equations with time-dependent constraints in a real Hilbert space. Moreover we apply our abstract results to a parabolic variational inequality with time-dependent double obstacles constraints.

Item Type:Preprint
Additional Information:10
Uncontrolled Keywords:Nonlinear evolution equation, subdifferential, parabolic PDE's, variational inequality
Subjects:34-xx ORDINARY DIFFERENTIAL EQUATIONS
47-xx OPERATOR THEORY
35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:865