# Some basic properties of bounded solutions of parabolic equations with p-Laplacian diffusion

## TL;DR

This paper rigorously derives fundamental properties of bounded weak solutions to initial-value problems involving p-Laplacian diffusion in parabolic equations, enhancing understanding of their behavior with bounded and integrable initial data.

## Contribution

It provides a detailed and rigorous derivation of key properties of solutions to p-Laplacian parabolic equations with bounded initial data, which was previously not fully established.

## Key findings

- Fundamental properties of solutions are rigorously derived.
- Results apply to general conservative second-order parabolic equations.
- Analysis covers solutions with bounded and integrable initial data.

## Abstract

We provide a detailed (and fully rigorous) derivation of several fundamental properties of bounded weak solutions to initial-value problems for general conservative 2nd-order parabolic equations with p-Laplacian diffusion and (arbitrary) bounded and integrable initial data.