Critical exponent for nonlinear damped wave equations with non-negative potential in 3D

TL;DR

This paper investigates how damping coefficients in a 3D wave equation influence the critical exponent for nonlinear solutions, revealing phenomena where certain coefficient relations cause significant jumps in critical exponents.

Contribution

It introduces new phenomena showing that specific relations between damping coefficients can cause large jumps in the critical Strauss exponent in 3D.

Findings

Certain damping coefficient relations cause the critical exponent to jump from 3D to 5D values.

The interaction of damping coefficients significantly affects the critical behavior of solutions.

The study highlights the impact of damping on the nonlinear wave equation's critical thresholds.

Abstract

We are studying possible interaction of damping coefficients in the subprincipal part of the linear 3D wave equation and their impact on the critical exponent of the corresponding nonlinear Cauchy problem with small initial data. The main new phenomena is that certain relation between these coefficients may cause very strong jump of the critical Strauss exponent in 3D to the critical 5D Strauss exponent for the wave equation without damping coefficients.