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

Authors

  • Bahloul Tarek

    math applied

  • Bouzit Mouhammed

Received date: December 2, 2012

Accepted date: December 15, 2012

Published date: January 1, 2015

DOI:

https://doi.org/10.14419/ijamr.v4i1.582

Keywords:

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.

Downloads

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: December 2, 2012

Accepted date: December 15, 2012

Published date: January 1, 2015