IJPAM: Volume 41, No. 5 (2007)

NONCLASSICAL SYMMETRIES AND DIRECT SIMILARITY
ANALYSIS OF A NONLOCAL GASEOUS IGNITION MODEL

R. Asokan$^1$, M. Pitchaimani$^2$
$^{1,2}$School of Mathematics
Madurai Kamaraj University
Tamil Nadu, Madurai, 625 021, INDIA
e-mail: rasoka_mku@yahoo.co.in


Abstract.The determining equations for the nonclassical reductions of a nonlocal gaseous ignition problem are obtained. It is shown that requiring compatibility with a first order quasilinear partial differential equation, the determining equations are also obtainable. Finally we discuss the similarity analysis of a nonlocal gaseous ignition problem by the direct method of Clarkson and Kruskal to obtain its similarity solution.

Received: August 17, 2007

AMS Subject Classification: 35K55, 34C14, 37L20, 70G65, 35F25, 53C70

Key Words and Phrases: nonlinear parabolic equation, determining equations, nonclassical symmetries, invariant surface condition, compatibility condition, quasilinear evolution equations, direct method and first integral

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 41
Issue: 5