Special Session 173: Mathematical and Numerical Analysis on Nonlinear PDEs

Lp-Lq estimates for evolution equations with damped oscillations
Marcello DAbbicco
University of Bari
Italy
Co-Author(s):    Marcelo Rempel Ebert
Abstract:
In this talk, we discuss $L^p-L^q$ estimates, with $1\leq p\leq q\leq\infty$, for dissipative wave-type equations, under the assumption that the dissipation dampens the oscillations but it does not cancel them. We employ methods based on Fourier analysis, including the use of real Hardy space $H^1(\mathbb{R}^n)$ and stationary phase arguments to take into account of the dispersive nature of the equation.