Waves in Flexural Beams with Nonlinear Adhesive Interaction

Abstract The paper studies the initial boundary value problem related to dynamic evolution of an elastic beam interacting with a substrate through elastic-breakable forcing term. This discontinuous interaction is aimed model phenomenon attachment-detachment occurring in adhesion phenomena. We prove existence solutions energy space and exhibit various counterexamples uniqueness. Furthermore we characterize some relevant features solutions, ruling main effects nonlinearity due term on dynamical evolution, by proving linearization property according Gérard (J Funct Anal 141(1):60–98, 1996) asymptotic result pertaining long time behavior.