Galerkin finite element method for a semi-linear parabolic equation with integral conditions
DOI:
https://doi.org/10.5269/bspm.44918Abstract
The present paper is devoted to prove the existence and uniquennes of a weak solution of a semi-linear reaction-difusion equation with only integral terms in the boundaries by using the finite element method and a priory
estimate.
References
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2. A. Bouziani, On a class of nonlinear reaction-Diffusion systems with nonlocal boudary conditions, A analysis 2004;9(2004) 793-813. https://doi.org/10.1155/S1085337504311061
3. A. Bouziani, Mixed problem with bouandary integral conditions for a certain parabolic equation, J. Appl. Math. Stochatic. Anal.9(1996) , no,323-330. https://doi.org/10.1155/S1048953396000305
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13. B. Nur-eddin and N. I. Yurchuk, A mixed problem with an integral condition for a parabolic equations with a Bessel operator, Differ. Uravn.27(1991), no. 12, 2094-2098.
14. C. V. Pao, Dynamics of reaction-diffusion equations with nonlocal boudary conditions, Quart Appl. Math.53 (1995), no1, 173-186. https://doi.org/10.1090/qam/1315454
15. C. V. Pao, Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boudary conditions, J. Comput. Appl. Math. 88(1998), no.1, 225-238. https://doi.org/10.1016/S0377-0427(97)00215-X
16. C. V. Pao, Numerical solutions of reaction-diffusion equations with nonlocal boudary conditions, J. Comput. Appl. Math. 136(2001), no.1-2, 227-243. https://doi.org/10.1016/S0377-0427(00)00614-2
17. N. I. Yurchuk, Amixed problem with an integral condition for some parablic equations, Differ. Urvan.22 (1986) no.12,21117-2126.
18. T-E Oussaeif and A. Bouziani, A priori estimates for weak solution for a time-fractional nonlinear reaction-diffusion equations with an integral condition, Chaos, Solitons & Fractals 103, 79-89 https://doi.org/10.1016/j.chaos.2017.05.035
19. E. DiBenedetto, M. Pierre, On the maximum principle for pseudoparabolic equations, Indiana Univ. Math. J. 30 (1981) 821-854. https://doi.org/10.1512/iumj.1981.30.30062
20. E. DiBenedetto, R. E. Showalter, Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12 (1981) 731-751. https://doi.org/10.1137/0512062
21. B. D. Coleman, R. J. Duffin, V. J. Mizel, Instability, uniqueness and non-existence theorems for the equation ut = uxx - uxtx on a strip, Arch. Rational Mech. Anal. 19 (1965) 100-116. https://doi.org/10.1007/BF00282277
22. A. Bouziani, Solvability of nonlinear pseudoparabolic equation with nonlocal boundary condition, Nonlinear Anal. 55 (2003) 883-904. https://doi.org/10.1016/j.na.2003.07.011
23. R. E. Showalter, T. W. Ting, Pseudo-parabolic partial differential operators, SIAM J. Math. Anal. 1 (1970) 1-26. https://doi.org/10.1137/0501001
2. A. Bouziani, On a class of nonlinear reaction-Diffusion systems with nonlocal boudary conditions, A analysis 2004;9(2004) 793-813. https://doi.org/10.1155/S1085337504311061
3. A. Bouziani, Mixed problem with bouandary integral conditions for a certain parabolic equation, J. Appl. Math. Stochatic. Anal.9(1996) , no,323-330. https://doi.org/10.1155/S1048953396000305
4. A. Bouziani, Mixed problems with bouandary integral conditionsfor certain partial differantial equations, ph.D thesis, constantine.
5. A. Bouziani, on a class of parabolic equation with a non local bouandary conditions , Acad. Roy.Belg. Bull. CI. .Sci.30(2002) , no, 1-6, 61-77. https://doi.org/10.3406/barb.1999.27977
6. A. Bouziani, On the solvability of parabolic and hyperbolic problems with a boudary integral condition, Int. J. Math. Math. Sci.31(2002), no4, 201-213. https://doi.org/10.1155/S0161171202005860
7. M. Dehghan, A finite difference method for a non-local boudary value problem for two dimensional heat equation, Appl. Math. Comput. 112(2000), no.1,133-142. https://doi.org/10.1016/S0096-3003(99)00055-7
8. M. Dehghan, Fully explicit finite-differencemethod for two-dimentional diffusion with an integral condition, nonlinear Anal.48 (2002), no.5,637,650. https://doi.org/10.1016/S0362-546X(00)00172-3
9. M. Dehghan, Fully explicit finite-difference methods for two-dimentional diffusion with an integral condition, Nonlinear Anal.48(2002), no.5,637-650. https://doi.org/10.1016/S0362-546X(00)00172-3
10. S. L. Hollis, R. H. Martin Jr, and M. Pierre, Global existence and boudeness in reaction-diffusion systems, Siam J. Math. Anal. 18 (1987), no3,744-761. https://doi.org/10.1137/0518057
11. S. L. Hollis and J. Morgan, Interior estimates for a class of reaction-diffusion systems from L1 a priori estimates in Mathematics, vol; 80,BSBB.G.Teubner Verlagsgesellschaft, Leipzig, 1985.
12. R. H. Martin Jr. and M. Pierre, Nonlinear reaction-diffusion systems, Nonlinear Equations in the applied sciences(W.F.Ames, C.Rogers, and Kapell, eds), Math, sci.Engrg, vol.185, Academic Pres s, Massachusetts, 1992, pp.363-398. https://doi.org/10.1016/S0076-5392(08)62804-0
13. B. Nur-eddin and N. I. Yurchuk, A mixed problem with an integral condition for a parabolic equations with a Bessel operator, Differ. Uravn.27(1991), no. 12, 2094-2098.
14. C. V. Pao, Dynamics of reaction-diffusion equations with nonlocal boudary conditions, Quart Appl. Math.53 (1995), no1, 173-186. https://doi.org/10.1090/qam/1315454
15. C. V. Pao, Asymptotic behavior of solutions of reaction-diffusion equations with nonlocal boudary conditions, J. Comput. Appl. Math. 88(1998), no.1, 225-238. https://doi.org/10.1016/S0377-0427(97)00215-X
16. C. V. Pao, Numerical solutions of reaction-diffusion equations with nonlocal boudary conditions, J. Comput. Appl. Math. 136(2001), no.1-2, 227-243. https://doi.org/10.1016/S0377-0427(00)00614-2
17. N. I. Yurchuk, Amixed problem with an integral condition for some parablic equations, Differ. Urvan.22 (1986) no.12,21117-2126.
18. T-E Oussaeif and A. Bouziani, A priori estimates for weak solution for a time-fractional nonlinear reaction-diffusion equations with an integral condition, Chaos, Solitons & Fractals 103, 79-89 https://doi.org/10.1016/j.chaos.2017.05.035
19. E. DiBenedetto, M. Pierre, On the maximum principle for pseudoparabolic equations, Indiana Univ. Math. J. 30 (1981) 821-854. https://doi.org/10.1512/iumj.1981.30.30062
20. E. DiBenedetto, R. E. Showalter, Implicit degenerate evolution equations and applications, SIAM J. Math. Anal. 12 (1981) 731-751. https://doi.org/10.1137/0512062
21. B. D. Coleman, R. J. Duffin, V. J. Mizel, Instability, uniqueness and non-existence theorems for the equation ut = uxx - uxtx on a strip, Arch. Rational Mech. Anal. 19 (1965) 100-116. https://doi.org/10.1007/BF00282277
22. A. Bouziani, Solvability of nonlinear pseudoparabolic equation with nonlocal boundary condition, Nonlinear Anal. 55 (2003) 883-904. https://doi.org/10.1016/j.na.2003.07.011
23. R. E. Showalter, T. W. Ting, Pseudo-parabolic partial differential operators, SIAM J. Math. Anal. 1 (1970) 1-26. https://doi.org/10.1137/0501001
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2022-01-24
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