On a third order parabolic equation with a nonlocal boundary condition

Journal of Applied Mathematics and Stochastic Analysis

Volumn 13, Issue 2, 2000, Pages 181-195

  Bouziani, Abdelfatah ^a  

^a UNIVERSITY OF OUM EL BOUAGHI   (Algeria)

Author keywords

A Priori Estimate; Integral Condition; Strong Solution; Third Order Parabolic Equation

Indexed keywords

EID: 0242387986     PISSN: 10489533     EISSN: 16872177     Source Type: Journal    
DOI: 10.1155/S1048953300000198     Document Type: Article

References (24)

1. Adams, R.A., Sobolev Spaces, Academic Press, New York 1975.
2. Batten, Jr., G.W., Second order correct boundary condition for the numerical solution of the mixed boundary problem for parabolic equations, Math. Comput. 17 (1963), 405-413.
3. Benouar, N.E. and Yurchuk, N.I., Mixed problem with an integral condition for parabolic equations with the Bessel operator, Differentsial'nye Uravneniya 27:12 (1991), 2094-2098.
4. Bouziani, A., Mixed problem for certain nonclassical equations with a small parameter, Bulletin de la Classe des Sciences, Académie Royale de Belgique 5 (1994), 389-400.
5. Bouziani, A., Problème aux limites pour certaines équations de type non classicque du troisième ordre, Bulletin de la Classe des Sciences, Académie Royale de Belgique 6 (1995), 215-222.
6. Bouziani, A., Mixed problem with integral conditions for a certain parabolic equation, J. of Appl. Math, and Stoch. Anal. 9:3 (1996), 323-330.
7. Bouziani, A., Mixed problem with nonlocal condition for certain pluriparabolic equations, Hiroshima Math. J. 27:3 (1997), 373-390.
8. Bouziani, A. and Benouar, N.E., Problème mixte avec conditions intégrales pour une classe d'équations parabliques, Comptes Rendus de l'Académie des Sciences, Paris 321:1 (1995), 1177-1182.
9. Bouziani, A. and Benouar, N.E., Problème mixte avec conditions intégrales pour une classe d'équations hyperboliques, Bulletin de la Société Math. de Belgique, 31 (1996), 125-133.
10. Bouziani, A. and Benouar, N.E., Problème aux limites pour une classe d'équations de type non classique pour une structure pluri-dimensionnelle, Bull. of the Polish Acad. of Sciences- Mathematics 43:4 (1995), 317-328.
11. Cahlon, B. and Kulkarni, D.M. and Shi, P., Stewise stability for the heat equation with a nonlocal constraint, SIAM J. Numer. Anal. 32:2 (1995), 571-593.
12. Cannon, J.R., The solution of the heat equation subject to the specification of energy, Quart. Appl. Math. 21:2 (1963), 155-160.
13. Cannon, J.R. and Van der Hoek, J., The existence and the continuous dependence for the solution of the heat equation subject to the specification of energy, Boll. Uni. Math. Ital. Suppl. 1 (1981), 253-282.
14. Cannon, J.R. and Van der Hoek, J., An implicit finite difference scheme for the diffusion of mass in a portion of the domain, Numer. Solutions of PDEs (ed. by J. Noye), North-Holland, Amsterdam (1982), 527-539.
15. Cannon, J.R., Esteva, S.P. and Van der Hoek, J., A Galerkin procedure for the diffusion equation subject to the specification of mass, SIAM J. Numer. Anal. 24 (1987), 499-515.
16. Gårding, L., Cauchy's Problem for Hyperbolic Equations, Univ. of Chicago Lecture Notes 1957.
17. Ionkin, N.I., Solution of boundary value problem in heat conduction theory with nonlocal boundary conditions, Differentsial'nye Uravneniya 13:2 (1977), 294-304.
18. Jones, S., Jumarhon, B., McKee, S. and Scott, J.A., A mathematical model of biosensor, J. Eng. Math. 30 (1996), 312-337.
19. Jumarhon, B. and McKee, S., On the heat equation with nonlinear and nonlocal boundary conditions, J. Math. Anal. Appl. 190 (1995), 806-820.
20. Jumarhon, B. and McKee, S., Product integration methods for solving a system of nonlinear Volterra integral equations, J. Comput. Appl. Math. 69 (1996), 285-301.
21. Kamynin, N.I., A boundary value problem in the theory of the heat conduction with non-classical boundary condition, Th. Vychisl. Mat. Mat. Fiz. 43:6 (1964), 1006-1024.
22. Rektorys, K., Variational Methods in Mathematics, Sciences and Engineering, 2nd ed., Dordrecht, Boston, Reidel 1979.
23. Shi, P., Weak solution to an evolution problem with a nonlocal constraint, SIAM. J. Math. Anal. 24:1 (1993), 46-58.
24. Yurchuk, N.I., Mixed problem with an integral condition for certain parabolic equations, Differentsial'nye Uravneniya 22:19 (1986), 2117-2126.