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Abstract quasi-variational inequalities of elliptic type and applications

100%

Murase Y.

Banach Center Publications

2009

tom 86

nr 1

235-246

A class of quasi-variational inequalities (QVI) of elliptic type is studied in reflexive Banach spaces. The concept of QVI was earlier introduced by A. Bensoussan and J.-L. Lions [2] and its general theory has been developed by many mathematicians, for instance, see [6, 7, 9, 13] and a monograph [1]. In this paper we give a generalization of the existence theorem established in [14]. In our treatment we employ the compactness method along with a concept of convergence of nonlinear multivalued operators of monotone type (cf. [11]). We shall prove an abstract existence result for our class of QVI's, and moreover, give some applications to QVI's for elliptic partial differential operators.

Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

51%

Kano R., Murase Y., Kenmochi N.

Banach Center Publications

2009

tom 86

nr 1

175-194

We consider an abstract formulation for a class of parabolic quasi-variational inequalities or quasi-linear PDEs, which are generated by subdifferentials of convex functions with various nonlocal constraints depending on the unknown functions. In this paper we specify a class of convex functions ${φ^t(v;·)}$ on a real Hilbert space H, with parameters 0 ≤ t ≤ T and v in a set of functions from [-δ₀,T], 0 < δ₀ < ∞, into H, in order to formulate an evolution equation of the form $u'(t) + ∂φ^t(u;u(t)) ∋ f(t)$, 0 < t < T, in H. Our objective is to discuss the existence question for the associated Cauchy problem.

Ograniczanie wyników

2 Banach Center Publications

2 Murase Y.

1 Kano R.

1 Kenmochi N.

2 2009

Wyniki wyszukiwania

Abstract quasi-variational inequalities of elliptic type and applications

Nonlinear evolution equations generated by subdifferentials with nonlocal constraints