Differential and Integral Equations

Unbounded solutions to defocusing parabolic systems

Delphine Côte

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 23 June 2015

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K15: Initial value problems for second-order parabolic equations 35C15: Integral representations of solutions 35Q56: Ginzburg-Landau equations


Côte, Delphine. Unbounded solutions to defocusing parabolic systems. Differential Integral Equations 28 (2015), no. 9/10, 899--940. https://projecteuclid.org/euclid.die/1435064544

Export citation