## Differential and Integral Equations

### Unbounded solutions to defocusing parabolic systems

Delphine Côte

#### Abstract

We give existence theorems for the Cauchy problem of a large class of semi-linear parabolic equations in $L^{\infty}$, $L^{\infty} \cap L^p$ or $L^{\infty} \cap \dot W^{1,p}$, using a contracting map argument. We then construct integral solutions to parabolic equations with data growing at infinity and defocusing nonlinearity, and give an example of instantaneous blow up when the nonlinearity is focusing and the initial data has tame growth.

#### Article information

Source
Differential Integral Equations, Volume 28, Number 9/10 (2015), 899-940.

Dates
First available in Project Euclid: 23 June 2015