ABSTRACT
In this chapter, the existence and asymptotic behavior of solutions to the second order evolution equation of monotone type is studied. Let A : D(A) ⊂ H → H be a maximal monotone operator. Consider the following second order evolution equation associated to A: () { p ( t ) u ″ ( t ) + q ( t ) u ′ ( t ) ∈ A u ( t ) , a .e . on ( 0 , + ∞ ) u ( 0 ) = u 0 ∈ D ( A ) , sup t ≥ 0 ‖ u ( t ) ‖ < + ∞ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429156908/6b59fc70-f121-4321-b34a-0baf5e3a2176/content/eq654.tif"/>
