Smooth Dynamics of Weakly Damped Lamé Systems with Delay
To Fu, Jaqueline G. Mesquita, Paulo N. Seminario‐Huertas
Abstract
The Lamé system is a classical model for isotropic elasticity and has important applications in seismology. In the present paper, we study the longtime dynamics of weakly damped Lamé systems that exhibit interior delay effects on the velocity. The main result establishes, under nonlinear forces of critical growth, the existence of a smooth finite dimensional global attractor. To the best of our knowledge, this result is new even for scalar wave equations.
Topics & Concepts
MathematicsAttractorIsotropyNonlinear systemScalar (mathematics)Mathematical analysisDynamics (music)Elasticity (physics)Classical mechanicsGeometryPhysicsQuantum mechanicsAcousticsThermodynamicsStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems