Strong solution for a high order boundary value problem with integral condition
The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem.
Strong solution for a high order boundary value problem with integral condition
The present paper is devoted to a proof of the existence and uniqueness of strong solution for a high order boundary value problem with integral condition. The proof is based by a priori estimate and on the density of the range of the operator generated by the studied problem.
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- Batten Jr, G. W.: Second-order correct boundary condition for the numerical solution of the mixed boundary problem for parabolic equation, Math. Comput. 17, 405–413 (1963).
- Bouziani, A., Benouar, N.E.: Mixed problem with integral conditions for third order parabolic equation, Kobe J. Math. 15 47–58 (1998).
- Cannarasa, P., Vespri, V.: On maximal Lp-regularity for abstract Cauchy problem, Boll. Unione Mat. Italiana 165–175 (1986).
- Cannon, J. R.: The solution of the heat equation subject to the specification of energy, Quart. Appl. Math. 21, 155–160 (1963).
- Cannon, J. R.: The one-dimensional heat equation, in Encyclopedia of Mathematics and its Applications, Vol. 23, Addison-Wesley, Menlo Park, CA, 1984.
- Cannon, J. R., Perez Esteva, S., Van Der Hoek, J.,: A Galerkin procedure for the diffusion equation subject to the specification of mass, Siam J. Numer. Anal. 24, 499–515 (1987).
- Choi, Y. S., Chan, K. Y.: A parabolic equation with nonlocal boundary conditions arising from electrochemistry, Nonlinear Anal. 18, 317–331 (1992).
- Denche, M., Marhoune, A. L.: Mixed problem with integral boundary conditions for a high order mixed type partial differential equation, J. Appl. Math. Stochastic Anal.16 (1), 69–79 (2003).
- Denche, M., Marhoune, A. L.: Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type, Int. J. Math. Sci. 26 (7), 417–426 (2001).
- Denche, M., Marhoune, A. L.: High-order mixed type partial differential equations with integral boundary conditions, Electron. J. Differ. Equ. (60), 1–10 (2000).
- Denche, M., Marhoune, A. L.: A three-point boundary value problem with an integral condition for parabolic equation with the Bessel operator, Appl. Math. Lett. 13, 85–89 (2000).
- Ewing, R. E., Lin, T.: A class of parameter estimation techniques for fluid flow in porous media, Adv. Water Resources 14, 89–97 (1991).
- Hardy, G. H., Littlewood, J. E., Polya, G.: Inequalities, Cambridge Press, Zbl 0010.10703 JFM 60.0169.01 1934. Hieber, M., Pruss, J.: Heat kernels and Maximal Lp-Lp estimates for parabolic evolution equation, Comm. Partial Differ. Equ. 22, 164761669 (1997).
- Ionkin, N. I.: Solution of a boundary-value problem in heat condition with a nonclassical boundary condition, Differ. Uravn. 13, 294–304 (1977).
- Kamynin, N. I.: A boundary value problem in the theory of the heat condition with non classical boundary condition, U. S. S. R. Comput. Math. Phys. 4, 33–59 (1964).
- Kartynnik, A. V.: Three-point boundary-value problem with an integral space-variable condition for a second-order parabolic equation, Differ. Equ. 26, 1160–1166 (1990).
- Marhoune, A. L.: A three-point boundary value problem with an integral two-space-variables condition for parabolic equations, Math. Comput. 53, 940–947 (2007).
- Marhoune, A. L., Bouzit, M.: High order differential equations with integral boundary condition, Far East J. Math. Sci. 18 (3), 341–450 (2005).
- Pruss, J., Simonett, G.: Maximal regularity for evolution equations in weighted Lp-spaces, Fachbereich Mathematic and Informatic, Martin-Luter-Universitat Halle-Wittenberg, July 2002.
- Samarskii, A. A.: Some problems in differential equations theory, Differ. Uravn. 16 (11), 1221–1228 (1980).
- Shi, P.: Weak solution to evolution problem with a nonlocal constraint, Siam J. Anal. 24, 46–58 (1993).
- Shi, P., Shillor, M.: Design of Contact patterns in One Dimensional Thermoelasticity, in: Theoretical Aspects of Industrial Design, Society for Industrial and Applied Mathematics, Philadelphia, PA,1992.
- Yurchuk, N. I.: Mixed problem with an integral condition for certain parabolic equations, Differ. Equ. 22, 1457–1463 (1986).