A third-order non-local problem with boundary integral condition for a parabolic equation

  • Authors

    • Bahloul Tarek math applied
    • Bouzit Mouhammed
    2015-01-01
    https://doi.org/10.14419/ijamr.v4i1.582
  • Integral Boundary Condition, Energy Inequalities, nonlocal condition.

  • Abstract

    The present paper is devoted to a proof of the existence and  uniqueness of a third-order non-local problem with boundary integral condition for a parabolic equation . The proof is based in two sided a priori estimates and the fact that the range of operator generalized by the considered problem is dense.

  • References

    1. [1] A. M .Al-kadhi, A Class of Hyperbolic Equations with Nonlocal Conditions, Int Journal of Math Analysis, 2 (2008) 491 – 498

      [2] A. Bouziani, Mixed problem with integral boundary condition for a certain parabolic equations , J Applied Mathematics and Stochastic Analysis, 6 )1996( 323-330.

      [3] A. Bouziani, N.E. Benouar, probléme mixte avec conditions intégrales pour une classe d'équations hyperboliques, Bull Belg Math Soc, 3 (1996)137-145.

      [4] L.Bougoffa, A third-order non-local problem with non local conditions, IJMMS , 28 )2004 (1503-1507.

      [5] M. Bouzit, N. Teyar, A Class of Third Order Parabolic Equations with Integral Conditions , Int Journal of Math Analysis, 3 )2009( 871 – 877.

      [6] M. Denche, On non-local problems for ordinary differential equations and on a non local parabolic transmission problem, Journal of Applied Mathematics and Stochastic Analysis, 12 (1999) 279-291.

      [7] M. Denche, A. L.Marhoune, High-order mixed-type differential equations with weighted integral boundary conditions , Electronic Journal of Differential Equations, 60 (2000) 1-10.

      [8] M. Denche, A. L. Marhoune, Mixed problem with integral boundary condition for a high order mixed type partial differential equation , J Appl Math Stochastic Anal, 16 (2003) 69-79.

      [9] M. Denche, A. L.Marhoune, Mixed problem with non local boundary conditions for a third-order partial differential equation of mixed type, Int J Math Sci, 26 (2001) 417-42.

      [10] M. Denche, A.Memou, Boundary value problem with integral conditions for a linear third-order equation, Journal of Applied Mathematics 11 (2003) 53–567.

      [11] S. Mesloub, A . Bouziani, On a class of singular hyperbolic equation with a weighted Iintegral condition, Int J math & math Sci, 22 (1999) 511-519.

      [12] S. Mesloub, A. Bouziani, N. Kechkar, A strong solution of an evolution problem with inyegral conditions, Georgian Mathematical Journal, 9 (2002) 149 -159.

      [13] N. I .Yurchuk, Mixed problem with an integral condition for certain parabolic equations, Diff Equ , 22 (1986) 1457-1463.

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  • How to Cite

    Tarek, B., & Mouhammed, B. (2015). A third-order non-local problem with boundary integral condition for a parabolic equation. International Journal of Applied Mathematical Research, 4(1), 15-23. https://doi.org/10.14419/ijamr.v4i1.582

    Received date: 2012-12-02

    Accepted date: 2012-12-15

    Published date: 2015-01-01