Inspired by [15], which considers the problem in Banach space, we continue to consider the existence of solutions for a nonlinear evolution inclusion in R N by relaxing the constraint conditions.
In [14], Xue-Cheng studied periodic problems for a nonlinear evolution inclusion, defined on an evolution triple of spaces, driven by a monotone operator, and with a perturbation term which is multivalued.
In this paper, we confine ourselves to the finite time blow-up property of solutions to Problem (1), an important property possessed by many nonlinear evolution equations.
Numerous contributions confirm that implicit Runge Kutta and linear multistep methods are favourable for the time discretisation of dynamic processes described by nonlinear evolution equations; as a small selection of literature we refer to [ 7, 15, 22, 37] and the references given therein.
The key ideas of the method are that the traveling wave solutions of a complicated nonlinear evolution equation can be constructed by means of various solutions of a second-order linear ordinary differential equation [20].
In fact, the approximate controllability of systems represented by nonlinear evolution equations has been studied by several authors.
Papageorgiou et al. [30] presented the sensitivity analysis for the optimal control problems governed by nonlinear evolution inclusions.
There have been some results as regards the controllability of systems represented by nonlinear evolution equations in infinite dimensional spaces [14 24].
It is well known that nonlinear phenomena occur in various areas of science and engineering, such as fluid mechanics, plasma, solid-state physics, biophysics, etc., and could be modeled by nonlinear evolution equations (NLEEs).
