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• # Artykuł - szczegóły

## Banach Center Publications

2009 | 86 | 1 | 175-194

## Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

EN

### Abstrakty

EN
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.

175-194

wydano
2009

### Twórcy

autor
• Department of Mathematics, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan
autor
• Department of Mathematics, Graduate School of Science and Technology, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan
autor
• Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan