Solvability of nonlinear evolution equations generated by subdifferentials and perturbations
Risei Kano, Yusuke Murase · Discrete and Continuous Dynamical Systems - S · 2013
The main objective of this paper is to discuss solvability of the Cauchy problem of an evolution equationwith subdifferentials of convex functions which is generated by unknown functions and perturbationsof the form: $ u'(t) + ∂ \varphi^t(u;u(t)) + G(u(t)) i f(t) $ 0 where H is a Hilbert space, $u'=\frac{du}{dt}$,and $∂ \varphi^t(u;\cdot )$ is a subdifferential operator of convex function $\varphi^t(u;\cdot )$.The evolution equation corresponds to parabolic quasi-variational inequalities.