Nonlinear evolution equations generated by subdifferentials with nonlocal constraints

• Autorzy: Risei Kano , Yusuke Murase , Nobuyuki Kenmochi
• Języki publikacji: 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.

Kategorie tematyczne

• 35K45: Initial value problems for second-order parabolic systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 86
• Numer: 1
• Strony: 175-194

Daty

wydano

2009

Twórcy

autor

Risei Kano

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

autor

Yusuke Murase

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

autor

Nobuyuki Kenmochi

• Department of Mathematics, Faculty of Education, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba, 263-8522 Japan

Identyfikatory

DOI

10.4064/bc86-0-11