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Journals / Hacettepe Journal of Mathematics and Statistics / 2008 / Volume: 37 Issue: 2

FOURIER METHOD FOR A QUASILINEAR PARABOLIC EQUATION WITH PERIODIC BOUNDARY CONDITION

I. Ciftci
H. Halilov
Pages
—
Publication Date
2008-02-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The existence, uniqueness and also continuity of the weak generalized solution is proved.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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).
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Key Findings & Data: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).
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Conclusion & Impact:The existence, uniqueness and also continuity of the weak generalized solution is proved.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Quasilinear parabolic equation · Mixed problem · Fourier method

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.

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Cite This Article

Ciftci, I., Halilov, H. (2008). FOURIER METHOD FOR A QUASILINEAR PARABOLIC EQUATION WITH PERIODIC BOUNDARY CONDITION. Hacettepe Journal of Mathematics and Statistics, Volume: 37 Issue: 2. https://ajindex.com/articles/1403765

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References (10)

  1. 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.
  2. Chandirov, G. I. On mixed problem for a class of quasilinear hyperbolic equation (PhD. Thesis, Tibilisi, 1970).
  3. Colton, D. The exterior Dirichlet problem for ∆3ut−ut+ ∆3u= 0. Appl. Anal. 7, 207–202, 1978.
  4. 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.
  5. Conzalez-Velasco, E. A. Fourier Analysis and Boundary Value Problems (Academic Press, New York, 1995).
  6. Halilov, H. On mixed problem for a class of quasilinear pseudoparabolic equation. Appl. Anal. 75 (1-2), 61–71, 2000.
  7. 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.
  8. 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).
  9. Rao, V. R. and Ting, T. W. F Initial-value problems for pseudoparabolic partial differential equations, Indiana Univ. Math. J. 23, 131–153, 1973.
  10. Rundell, W. The solution of initial- boundary value problems for pseudoparabolic partial differential equations, Proc. Roy. Soc. Edin. Sect. A. 74, 311–326, 1975.