American Institute of Mathematical Sciences

February  2014, 7(1): 75-93. doi: 10.3934/dcdss.2014.7.75

Solvability of nonlinear evolution equations generated by subdifferentials and perturbations

 1 Faculty of Education, Kochi University, 2-5-1 Akebono-cho, Kochi 780-8520, Japan 2 Department of Mathematics, Faculty of Science and Technology, Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya, 468-8502

Received  March 2012 Revised  October 2012 Published  July 2013

The main objective of this paper is to discuss solvability of the Cauchy problem of an evolution equation with subdifferentials of convex functions which is generated by unknown functions and perturbations of the form:
$u'(t) + ∂ \varphi^t(u;u(t)) + G(u(t)) \ni f(t)$   0 < t < T,      in     H.
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.
Citation: Risei Kano, Yusuke Murase. Solvability of nonlinear evolution equations generated by subdifferentials and perturbations. Discrete & Continuous Dynamical Systems - S, 2014, 7 (1) : 75-93. doi: 10.3934/dcdss.2014.7.75
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