Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations
The author establishes strong lower energy estimates for strong solutions of nonlinearly damped Timoshenko beams, Petrowsky equations in two and three dimensions and wave-like equations for bounded one-dimensional domains or annulus domains in two or three dimensions. Weak lower velocity estimates for strong solutions of the nonlinearly damped Petrowsky equation are also established. In a previous paper [J. Differ. Equations 249, No. 5, 1145--1178 (2010; Zbl 1201.35042)], the author showed that it is possible to derive strong lower energy estimates for general dampings, localized as well as boundary dampings under weaker regularity assumptions on the initial data. The weak lower velocity estimates of Haraux are also extended to general dampings and multidimensional domains for bounded velocities in time and spaces.
scientific article; zbMATH DE number 5982607
scientific article