## Differential and Integral Equations

### A Phragmén-Lindelöf alternative for a class of quasilinear second order parabolic problems

#### Abstract

This paper deals with classical solutions of quasilinear equations of the form $$[\rho(\mathbf{x},t,u,\nabla u)u,_i],_i = u,_t$$ in a semi--infinite cylinder in $\Bbb R^3$ with homogeneous initial data and with homogeneous Dirichlet data prescribed on the lateral surface for all time. Under appropriate assumptions on the form of $\rho$, Phragmen--Lindelöf type growth--decay estimates are derived.

#### Article information

Source
Differential Integral Equations, Volume 8, Number 3 (1995), 539-551.

Dates
First available in Project Euclid: 23 May 2013

https://projecteuclid.org/euclid.die/1369316504

Mathematical Reviews number (MathSciNet)
MR1306573

Zentralblatt MATH identifier
0833.35018

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Secondary: 35K55: Nonlinear parabolic equations

#### Citation

Lin, Chang Hao; Payne, L. E. A Phragmén-Lindelöf alternative for a class of quasilinear second order parabolic problems. Differential Integral Equations 8 (1995), no. 3, 539--551. https://projecteuclid.org/euclid.die/1369316504