Über Maximale Monotonie von Operatoren des Typs L*ϕ·L

Regular solutions of wave equations containing nonlinearities of the type L Φ L

“…The potential results are a consequence of a theorem of Vainberg [12, p. 56]. In order to conclude the maximal cyclical monotonicity of L$>L, it is sufficient that <& has this property [13,14]. The maximality of $ is a consequence of the fact that $ is hemi-continuous and D(O) = H.…”

“…In the space H = L 2 (il), the model is given by u t t +A 2 u-/ |gradu| 2 d£ Au = r(x). (13) with boundary conditions u(x, t) = Au(x, t) = 0 for xedil and u(x, 0) = <p(x) as well as u,(x, 0) = ip(x) for x e Cl. Here, SI is a bounded domain in R 2 (or IR m ) and, in consequence, the operator grad u has a bounded inverse for MGHj(il).…”

“…Nonlinear wave equations and eigenvalue problems containing nonlinear operators /((AM, M))AU have been considered by Bazley et al [1,2,3]. In the papers [13,14], the author gave preference to the decomposition of form LQ>L, because this aspect of the operators considered allows the proof of maximal (cyclical) monotonicity, if $ is maximal (cyclically) monotone.…”