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Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

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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

1 Banach Center Publications

1 Kano R.

1 Kenmochi N.

1 Murase Y.

1 2009

Wyniki wyszukiwania

Nonlinear evolution equations generated by subdifferentials with nonlocal constraints