J. Nonl. Evol. Equ. Appl. 2013 (1), pp. 1-9, published on January 31, 2013:

Some properties of the fundamental solutions of non-stationary third order composite type equation in multidimensional domains


A. R. Khashimov

Tashkent Financial Institute, Tashkent, Uzbekistan

Received on April 10, 2012
Accepted on June 21, 2012 (with modifications), July 3, 2012 (2nd revised version)

Communicated by Michael Ruzhansky

Abstract.  Some basic properties for fundamental solutions of non-stationary third order composite type equation are studied in the neighborhood of some hyperplane of the domain in which fundamental solutions irregular. These properties give possibility to construct the classical solution of the Cauchy problem and the boundary value problems by a method of potentials.
Keywords: composite type, fundamental solutions, non-stationary equation, boundary value problems, solution, multidimensional domain.
2010 Mathematics Subject Classification:   35M99.

Download Full Text: JNEEA-vol.2013-no.1.pdf [216 kB].


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