Special Session 173: Mathematical and Numerical Analysis on Nonlinear PDEs

Global Weak Solutions to Nonlinear Wave Equations with Damping under Fractional Derivative Control
Hideo Kubo
Hokkaido University
Japan
Co-Author(s):    Bushra Nisar
Abstract:
In this talk we present a result on the initial-boundary value problem for the wave equation with nonlinear damping and source terms prescribed the nonhomogeneous Neumann boundary condition involved time fractional derivative of solution. In the pioneering work of Professors Georgiev and Todorova (1994), existence of global weak solution exists for homogeneous Dirichret boundary value problem, provided the damping term is dominated to the source term in some sense. On the other hand, a recent work of Mbodje(2004) consider the linear wave equation with the time fractional Neumann boundary condition in one space dimension. Out purpose is simply to extend the latter result to the nonlinear setting as in the former work.