Critical exponents and where to find them

Abstract

In this expository paper we present a list of different semilinear wave-type problems with time-variable coefficients. The aim of this work is to understand the influence of such coefficients on the critical exponents for polynomial nonlinearities. Statements of global existence and blow-up will follow according to exponents which are below or above these critical ones.

Keywords

• semilinear wave equations
• time variable coefficients
• critical exponents