On some evolution inequalities in a Hilbert space
In this -- rather technical note -- the author gives some evolution inequalities related to Sobolev type evolution equations. Such inequalities are used to study the uniqueness and asymptotic growth of solutions to differential inequalities of the form \[ \|B(t)u'(t) - A(t)u(t)\|\leq F(t,p(t),q(t)) \] and \[ \|B(t)u'(t) + M(t)u(t) - A(t)u(t)\|\leq G(t,p(t),q(t)), \] where \(B(t)\), \(A(t)\), \(M(t)\) are linear operators acting on a Hilbert space and \(p\), \(q\) , \(F\), \(G\) are suitable functions.
scientific article; zbMATH DE number 1496346
scientific article