Paper Information

Journal:   IRANIAN JOURNAL OF MATHEMATICAL SCIENCES AND INFORMATICS (IJMSI)   2014 , Volume 9 , Number 1; Page(s) 1 To 12.
 
Paper: 

THE WAVE EQUATION IN NON-CLASSIC CASES: NON-SELF ADJOINT WITH NON-LOCAL AND NON-PERIODIC BOUNDARY CONDITIONS

 
 
Author(s):  JAHANSHAHI MOHAMMAD*, AHMADKHANLU ASGHAR
 
* AZARBAIJAN SHAHID MADANI UNIVERSITY, TABRIZ, IRAN
 
Abstract: 

In this paper the wave equation in some non-classic cases has been studied. In the first case boundary conditions are non-local and non- periodic. At that case the associated spectral problem is a self-adjoint problem and consequently the eigenvalues are real. But in the second case the associated spectral problem is non-self-adjoint and consequently the eigenvalues are complex numbers, in which two cases, the solutions of the problem are constructed by the Fourier method. By compatibility conditions and asymptotic expansions of the Fourier coefficients, the convergence of series solutions are proved.
Finally, series solutions are established and the uniqueness of the solution is proved by a special way which has not been used in classic texts.

 
Keyword(s): WAVE EQUATION, NON-LOCAL & NON-PERIODIC BOUNDARY CONDITIONS, ASYMPTOTIC EXPANSION
 
References: 
 
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