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2004 Singular perturbations for parabolic equations with unbounded coefficients leading to ultraparabolic equations
Denis R. Akhmetov, Mikhail M. Lavrentiev Jr., Renato Spigler
Differential Integral Equations 17(1-2): 99-118 (2004).

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 $t=0$.

Citation

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Denis R. Akhmetov. Mikhail M. Lavrentiev Jr.. Renato Spigler. "Singular perturbations for parabolic equations with unbounded coefficients leading to ultraparabolic equations." Differential Integral Equations 17 (1-2) 99 - 118, 2004.

Information

Published: 2004
First available in Project Euclid: 21 December 2012

zbMATH: 1164.35312
MathSciNet: MR2035497

Subjects:
Primary: 35K70
Secondary: 35B25 , 35F30 , 35K20

Rights: Copyright © 2004 Khayyam Publishing, Inc.

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Vol.17 • No. 1-2 • 2004
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