Further Analysis on Classifications of PDE(S) with Variable Coefficients
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Applied Mathematics Letters 23 (2010) 966–970 Contents lists available at ScienceDirect Applied Mathematics Letters journal homepage: www.elsevier.com/locate/aml Further analysis on classifications of PDE(s) with variable coefficients A. Kılıçman a,∗, H. Eltayeb b, R.R. Ashurov c a Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia b Mathematics Department, College of Science, King Saud University, P.O.Box 2455, Riyadh 11451, Saudi Arabia c Institute of Advance Technology, Universiti Putra Malaysia, 43400 UPM, Serdang, Selangor, Malaysia article info a b s t r a c t Article history: In this study we consider further analysis on the classification problem of linear second Received 1 April 2009 order partial differential equations with non-constant coefficients. The equations are Accepted 13 April 2010 produced by using convolution with odd or even functions. It is shown that the patent of classification of new equations is similar to the classification of the original equations. Keywords: ' 2010 Elsevier Ltd. All rights reserved. Even and odd functions Double convolution Classification 1. Introduction The subject of partial differential equations (PDE's) has a long history and a wide range of applications. Some second- order linear partial differential equations can be classified as parabolic, hyperbolic or elliptic in order to have a guide to appropriate initial and boundary conditions, as well as to the smoothness of the solutions. If a PDE has coefficients which are not constant, it is possible that it is of mixed type.
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