Exponential convergence to steady-states for trajectories of a damped dynamical system modeling adhesive strings
We study the global well-posedness and asymptotic behavior for a semilinear damped wave equation with Neumann boundary conditions, modeling a one-dimensional linearly elastic body interacting with a rigid substrate through an adhesive material. The key feature of of the problem is that the interplay between the nonlinear force and the boundary conditions allows for a continuous set of equilibrium points. We prove an exponential rate of convergence for the solution towards a (uniquely determined) equilibrium point.
WOS:001207672300001
2024-04-20
REVIEWED
Funder | Grant Number |
Italian Ministry of University and Research under the Programme "Department of Excellence" | CUP D93C23000100001 |
INdAM-GNAMPA 2023 Project | CUP E53C22001930001 |
Research Project of National Relevance - Italian Ministry of Education, University and Research(MIUR PRIN) | 2022M9BKBC |
National Recovery and Resilience Plan (NRRP) of Italian Ministry of University and Research - European Union (NextGenerationEU Award) | 3138 |
Swiss State Secretariat for Education, Research and Innovation (SERI) | MB22.00034 |
Research for Innovation (REFIN), POR Puglia FESR FSE | CUP D94I20001410008 |
Alexander von Humboldt-Professorship program | |
ModConFlex Marie Curie Action | HORIZON-MSCA-2021-DN-01 |
COST Action MAT-DYN-NET | |
Transregio 154 Project of the DFG | PID2020-112617GB-C22 |
MINECO (Spain) | TED2021-131390B-I00 |
Madrid Goverment - UAM Agreement for the Excellence of the University Research Staff | |