A new approach of strong stabilization of distributed systems
The author considers the Dirichlet initial-boundary value problem for the equation \(u'' - \Delta u + g(u') = 0\). His aim is to minimize the requirements guaranteeing the decay of energy solutions to zero for \(t \to +\infty \) by separating them from the assumptions ensuring the existence and uniqueness of solutions. Hence, his results weaken considerably usual assumptions and include functions \(g\) that are not monotone, have not polynomial growth near the origin and the domains of spatial variables \(\Omega \) of finite measure, not necessarily bounded. The author then extends the results to the above wave equation with additional terms either of the form \(f(u)\) or \(-\Delta u'\). The plate equation \(u'' + \Delta ^2 u - g(\Delta u') = 0\) is dealt with as well.
Dirichlet initial-boundary value problem
scientific article; zbMATH DE number 1453638