Abstract
References
- Amiraliyev, G. M. and Mamedov, Y. D. Difference scheme on the uniform mesh for singular perturbed pseudoparabolic equations. Turk. J. of Mathematics 19, 207–222, 1995.
- Chandirov, G. I. On mixed problem for a class of quasilinear hyperbolic equation (PhD. Thesis, Tibilisi, 1970).
- Colton, D. The exterior Dirichlet problem for ∆3ut−ut+ ∆3u= 0. Appl. Anal. 7, 207–202, 1978.
- 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.
- Conzalez-Velasco, E. A. Fourier Analysis and Boundary Value Problems (Academic Press, New York, 1995).
- Halilov, H. On mixed problem for a class of quasilinear pseudoparabolic equation. Appl. Anal. 75 (1-2), 61–71, 2000.
- 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.
- Hasanov, K. K. On solution of mixed problem for a quasilinear hiperbolic and parabolic equation(PhD. Thesis, Baku, 1961). [9] IL’in, V. A. Solvability of mixed problem for hyperbolic and parabolic equation, Uspekhi Math. Nauk, 15:2, 92, 97–154, 1960. [10] Ladyzhenskaya, D. A. Boundary Value Problems of Mathematical Physics (Springer, New York, 1985).
- Rao, V. R. and Ting, T. W. F Initial-value problems for pseudoparabolic partial differential equations, Indiana Univ. Math. J. 23, 131–153, 1973.
- Rundell, W. The solution of initial- boundary value problems for pseudoparabolic partial differential equations, Proc. Roy. Soc. Edin. Sect. A. 74, 311–326, 1975.
Abstract
A multidimensional mixed problem with Neuman type periodic boundary condition is studied for the quasilinear parabolic equation ∂u
∂t −
a
2 ∂
2u
∂x2 = f(t, x, u). The existence, uniqueness and also continuity of
the weak generalized solution is proved.
Keywords
Quasilinear parabolic equation Mixed problem Fourier method Periodic boundary condition Generalized solutions
References
- Amiraliyev, G. M. and Mamedov, Y. D. Difference scheme on the uniform mesh for singular perturbed pseudoparabolic equations. Turk. J. of Mathematics 19, 207–222, 1995.
- Chandirov, G. I. On mixed problem for a class of quasilinear hyperbolic equation (PhD. Thesis, Tibilisi, 1970).
- Colton, D. The exterior Dirichlet problem for ∆3ut−ut+ ∆3u= 0. Appl. Anal. 7, 207–202, 1978.
- 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.
- Conzalez-Velasco, E. A. Fourier Analysis and Boundary Value Problems (Academic Press, New York, 1995).
- Halilov, H. On mixed problem for a class of quasilinear pseudoparabolic equation. Appl. Anal. 75 (1-2), 61–71, 2000.
- 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.
- Hasanov, K. K. On solution of mixed problem for a quasilinear hiperbolic and parabolic equation(PhD. Thesis, Baku, 1961). [9] IL’in, V. A. Solvability of mixed problem for hyperbolic and parabolic equation, Uspekhi Math. Nauk, 15:2, 92, 97–154, 1960. [10] Ladyzhenskaya, D. A. Boundary Value Problems of Mathematical Physics (Springer, New York, 1985).
- Rao, V. R. and Ting, T. W. F Initial-value problems for pseudoparabolic partial differential equations, Indiana Univ. Math. J. 23, 131–153, 1973.
- Rundell, W. The solution of initial- boundary value problems for pseudoparabolic partial differential equations, Proc. Roy. Soc. Edin. Sect. A. 74, 311–326, 1975.
Details
| Primary Language | English |
|---|---|
| Subjects | Statistics |
| Journal Section | Mathematics |
| Authors | |
| Publication Date | February 1, 2008 |
| Published in Issue | Year 2008 Volume: 37 Issue: 2 |