IJPAM: Volume 52, No. 5 (2009)

FOURIER METHOD FOR A QUASILINEAR
PSEUDO-PARABOLIC EQUATION WITH
PERIODIC BOUNDARY CONDITION

Huseyin Halilov$^1$, Irem Çiftçi$^2$
$^1$Department of Mathematics
Rize University
Rize, TURKEY
e-mail: huseyin.halilov@rize.edu.tr
$^2$Department of Mathematics
Kocaeli University
Umuttepe Campus
Kocaeli, 41380, TURKEY
e-mail: isakinc@kocaeli.edu.tr


Abstract.A multidimensional mixed problem with Neuman type periodic boundary condition is studied for quasilinear pseudo-parabolic equation $\frac{%
\partial u}{\partial t}-a^{2}\frac{\partial ^{2}u}{\partial x^{2}}%
-\varepsilon \frac{\partial ^{3}u}{\partial t\partial
x^{2}}=f(t,x,u).$ The existence, uniqueness and also convergence of the weak generalized solution is proved.

Received: April 17, 2009

AMS Subject Classification: 35K55,35K70

Key Words and Phrases: quasilinear parabolic equation, mixed problem, Fourier method, periodic boundary condition, generalized solutions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 52
Issue: 5