Numerical Solution of a Quasilinear Parabolic Problem with Periodic Boundary Condition

References (12)

1. Bouziani, A. and Mesloub, S. Mixed problem with a weighted integral condition for a para- bolic equation with the Bessel operator, Jour. of Appl. Math. and Stoc. Anal. 15 (3), 277–286, 2002.
2. Liu, C. Weak solutions for a viscous p-Laplacian equation, Elec. Jour. Diff. Equation 63, 1–11, 2003.
3. Colton, D and Wimp, J. Asymptotic behaviour of the fundamental solution to the equation of heat conduction in two temperature, J. Math. Anal. Appl. 2, 411–418, 1979.
4. Ciftci, I. and Halilov, H. Fourier method for a quasilinear parabolic equation with periodic boundary condition, Hacettepe J. Math. Stat. 37 (2), 69–79, 2008.
5. Egger, H., Engl, H. W. and Klibanov, M. V. Global uniquenes and H¨older stability for re- covering a nonlinear source term in a parabolic equation(Aus. Nat. Scien. Foun. 013 (08), 2001), Inverse Problems 21 (1), 271–290, 2005.
6. Halilov, H. On mixed problem for a class of quasilinear pseudo - parabolic equations, Journal of Kocaeli Univ., Pure and Applied Math. Sec. 3, 1–7, 1996.
7. Halilov, H. On mixed problem for a class of quasilinear pseudoparabolic equation, Appl. Anal. 75 (1-2), 61-71, 2000.
8. Hasanov, K. K. On solution of mixed problem for a quasilinear hiperbolic and parabolic equation(Ph.D. Thesis, Baku, 1961). Il’in, V. A. Solvability of mixed problem for hyperbolic and parabolic equation, Uspekhi Math. Nauk 15: 2 (92), 97–154, 1960.
9. Kassam, A. and Trefethen, L. N. Fourth-order time-stepping for stiff PDEs, SIAM J. Sci. Comput. 26 (4), 1214–1233, 2005.
10. Rao, V. R. and Ting, T. W. Initial-value problems for pseudoparabolic partial differential equations, Indiana Univ. Math. J. 23, 131–153, 1973.
11. Rundell, W. The solution of initial- boundary value problems for pseudoparabolic partial differential equations, Proc. Roy. Soc. Edin. Sect. A. 74, 311–326, 1975.
12. Samarski, A. A. The theory of difference schemes (Marcel Dekker, New York, 2001).