# Classification of the blow-up behavior for a semilinear wave equation with nonconstant degenerate coefficients

## TL;DR

This paper investigates the blow-up behavior and regularity of solutions for a nonlinear wave equation with nonconstant, degenerate coefficients, addressing challenges posed by variable wave speeds.

## Contribution

It provides new insights into blow-up phenomena and regularity for wave equations with degenerate, nonconstant coefficients, including partial results at degeneracy points.

## Key findings

- Characterization of blow-up behavior
- Analysis of blow-up set regularity
- Partial results at degeneracy points

## Abstract

We consider a nonlinear wave equation with nonconstant coefficients. In particular, the coefficient in front of the second order space derivative is degenerate. We give the blow-up behavior and the regularity of the blow-up set. Partial results are given at the origin, where the degeneracy occurs. Some nontrivial obstacles, due to the nonconstant speed of propagation, have to be surmounted.