# Large time behavior of solutions for a Cauchy problem on nonlinear conservation laws with large initial data in the whole space

## TL;DR

This paper investigates the long-term behavior of solutions to nonlinear conservation laws with large initial data, establishing global existence and decay estimates using advanced analytical techniques.

## Contribution

It provides new results on the global existence and decay rates for solutions with large initial data in nonlinear conservation laws.

## Key findings

- Proved global existence of solutions with large initial data.
- Established optimal decay estimates over time.
- Applied Green's function, Fourier analysis, and pseudo-differential operators.

## Abstract

We consider the Cauchy problem on a nonlinear conversation law with large initial data. By Green's function methods, energy methods, Fourier analysis, frequency decomposition, pseudo-differential operators, we obtain the global existence and the optimal decay estimate of $t$.

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Source: https://tomesphere.com/paper/1706.08121