Decay of energy for second-order boundary hemivariational inequalities with coercive damping

作者：Kalita Piotr^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(4): 1164-1181.

DOI：10.1016/j.na.2010.09.053

• Hemivariational inequality
• Asymptotic behavior
• Exponential decay of energy
• Coercive damping

In this article we consider the asymptotic behavior of solutions to second-order evolution inclusions with the boundary multivalued term u''(t) + A(t, u'(t)) + Bu(t) + (gamma) over bar*partial derivative J(t, (gamma) over baru'(t)) there exists 0, and u''(t) + A(t, u'(t)) + Bu(t) + (gamma) over bar*partial derivative J(t, (gamma) over baru(t)) there exists 0, where A is a (possibly) nonlinear coercive and pseudomonotone operator, B is linear, continuous, symmetric and coercive, (gamma) over bar is the trace operator and J is a locally Lipschitz integral functional with. denoting the Clarke generalized gradient taken with respect to the second variable. For both cases we provide conditions under which the appropriately defined energy decays exponentially to zero as time tends to infinity. We discuss assumptions and provide examples of multivalued laws that satisfy them.

• 出版日期2011-2-15