## Differential and Integral Equations

### Singular perturbations for parabolic equations with unbounded coefficients leading to ultraparabolic equations

#### Abstract

Linear parabolic equations with coefficients of the lower-order terms unbounded, and with a small parameter multiplying some of the second (highest) space derivatives are considered, in the limiting case when such a parameter goes to zero. This yields a degenerate parabolic (ultraparabolic) equation with one space-like variable, $x$, and two time-like variables, $y$ and $t$. No boundary-layer is found to be needed in the case of the boundary-value problem on the $x$-unbounded domain $\mathcal{Q}_T=\{(x,y,t)\in \mathbb{R}\times [0,1]\times[0,T]\}$ with a periodic boundary condition in the variable $y$ and initial data at $t=0$.

#### Article information

Source
Differential Integral Equations Volume 17, Number 1-2 (2004), 99-118.

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356060474

Mathematical Reviews number (MathSciNet)
MR2035497

Zentralblatt MATH identifier
1164.35312

#### Citation

Akhmetov, Denis R.; Lavrentiev, Mikhail M.; Spigler, Renato. Singular perturbations for parabolic equations with unbounded coefficients leading to ultraparabolic equations. Differential Integral Equations 17 (2004), no. 1-2, 99--118. https://projecteuclid.org/euclid.die/1356060474.