2026-06-01T02:29:37Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/499422023-08-27T10:15:51Zcom_20.500.14352_14col_20.500.14352_15

Asymptotics for some nonlinear damped wave equation: finite time convergence versus exponential decay results Díaz Díaz, Jesús Ildefonso Baji, B. Cabot, Alexandre 517.91 solid friction motion damped wave equation dry friction second-order differential inclusion finite time extinction exponential decay Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias Given a bounded open set Omega subset of R-n and a continuous convex function Phi: L-2(Omega) -> R, let us consider the following damped wave equation u(tt) - Delta u + partial derivative Phi(u(t)) 0, (t, x) is an element of (0, +infinity) x Omega, (S) under Dirichlet boundary conditions. The notation partial derivative Phi refers to the subdifferential of Phi in the sense of convex analysis. The nonlinear term partial derivative Phi allows to modelize a large variety of friction problems. Among them, the case Phi = vertical bar.vertical bar L-1 corresponds to a Coulomb friction, equal to the opposite of the velocity sign. After we have proved the existence and uniqueness of a solution to (S), our main purpose is to study the asymptotic properties of the dynamical system (S). In two significant situations, we bring to light an interesting phenomenon of dichotomy: either the solution converges in a finite time or the speed of convergence is exponential as t -> +infinity. We also give conditions which ensure the finite time stabilization of (S) toward some stationary solution. DGISGPI (Spain). EU Depto. de Análisis Matemático y Matemática Aplicada Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T09:34:30Z 2023-06-20T09:34:30Z 2007-11 journal article https://hdl.handle.net/20.500.14352/49942 0294-1449 10.1016/j.anihpc.2006.10.005 eng MTM2005-03463 RTN HPRN-CT-2002-00274 restricted access application/pdf Elsevier (Gauthier-Villars),