Formation of Multi-Point Singularities of Self-Similar Type for Burgers Equation

TL;DR

This paper constructs and analyzes multi-point self-similar blowup solutions for the inviscid Burgers equation, detailing their shape, dynamics, and stability under small initial perturbations.

Contribution

It introduces a method to construct stable multi-point self-similar blowup solutions for the inviscid Burgers equation, advancing understanding of singularity formation.

Findings

Multi-point blowup solutions are explicitly constructed.

The solutions' shape and blowup dynamics are precisely characterized.

Constructed solutions are stable under small initial data perturbations.

Abstract

In this paper, we constuct the multi-point blowup solutions of self-similar type for the inviscid Burgers equation. The shape and blowup dynamics are precisely described. Moreover, the solutions we construct are stable under small perturbations on initial data restricted in a compact set.