# Singular p-Laplacian parabolic system in exterior domains: higher regularity of solutions and related properties of extinction and asymptotic behavior in time

## TL;DR

This paper investigates the regularity, extinction, and decay properties of solutions to a p-Laplacian parabolic system in exterior domains, providing new insights into their long-term behavior and boundary regularity.

## Contribution

It establishes higher regularity of solutions up to the boundary and characterizes extinction and exponential decay phenomena for specific p ranges.

## Key findings

- Proves boundary regularity of solutions
- Identifies extinction conditions for p in a specific range
- Shows exponential decay when p equals a critical value

## Abstract

We consider the IBVP in exterior domains for the p-Laplacian parabolic system. We prove regularity up to the boundary, extinction properties for p \in ( 2n/(n+2) , 2n/(n+1) ) and exponential decay for p= 2n/(n+1) .