A finite difference approach to the number of peaks of solutions for semilinear parabolic problems

Masahisa TABATA

doi:10.2969/jmsj/03210171

Masahisa TABATA

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JOURNAL FREE ACCESS

1980 Volume 32 Issue 1 Pages 171-192

DOI https://doi.org/10.2969/jmsj/03210171

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Published: 1980 Received: June 10, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Chafee, Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, J. Differential Equations, 18 (1975), 111-134.
2) A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, 1964.
3) M. Ito, The conditional stability of stationary solutions for Semilinear parabolic differential equations, J. Fac. Sci. Univ. Tokyo, 25 (1978), 263-275.
4) H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ., 18 (1978), 221-227.
5) H. Matano, Asymptotic behavior and stability of solutions of semilinear diffusion equations, to appear in Publ. Res. Inst. Math. Sci.
6) M. Mimura, Asymptotic behaviors of a parabolic system related to a planktonic prey and predator model, to appear in SIAM J. Appl. Math.
7) T. Nakagawa, Blowing up of a finite difference solution to u_t=u_xx+u², Applied Mathematics and Optimization, 2 (1976), 337-350.
8) M. Tabata, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18 (1978), 327-351.

Right : [1] N. Chafee, Asymptotic behavior for solutions of a one-dimensional parabolic equation with homogeneous Neumann boundary conditions, J. Differential Equations, 18 (1975), 111-134.
[2] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, 1964.
[3] M. Ito, The conditional stability of stationary solutions for semilinear parabolic differential equations, J. Fac. Sci. Univ. Tokyo, 25 (1978), 263-275.
[4] H. Matano, Convergence of solutions of one-dimensional semilinear parabolic equations, J. Math. Kyoto Univ., 18 (1978), 221-227.
[5] H. Matano, Asymptotic behavior and stability of solutions of semilinear diffusion equations, to appear in Publ. Res. Inst. Math. Sci.
[6] M. Mimura, Asymptotic behaviors of a parabolic system related to a planktonic prey and predator model, to appear in SIAM J. Appl. Math.
[7] T. Nakagawa, Blowing up of a finite difference solution to u_t=u_xx+u², Applied Mathematics and Optimization, 2 (1976), 337-350.
[8] M. Tabata, Uniform convergence of the upwind finite element approximation for semilinear parabolic problems, J. Math. Kyoto Univ., 18 (1978), 327-351.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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