Numerical existence and uniqueness proof for solutions of semilinear parabolic equations

Applied Mathematics Letters

Volumn 14, Issue 6, 2001, Pages 707-714

  Minamoto, T ^a  

^a SAGA UNIVERSITY   (Japan)

Author keywords

Numerical verification; Parabolic equation

Indexed keywords

EID: 0035427474     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0893-9659(01)80031-8     Document Type: Article

References (7)

1. Minamoto T., Nakao M.T. Numerical verifications of solutions for nonlinear parabolic equations in one-space dimensional case. Reliable Computing. 3:1997;137-147.
2. Zeidler E. Nonlinear Functional Analysis and its Applications II/A. 1990;Springer.
3. T. Minamoto, Numerical existence and uniqueness proof for solutions of nonlinear hyperbolic equations, (preprint).
4. Yamamoto N. A numerical verification method for solutions of boundary value problems with local uniqueness by Banach's fixed point theorem. SIAM Journal on Numerical Analysis. 35:1998;2004-2013.
5. Adams R.A. Sobolev Spaces. 1978;Academic Press.
6. Minamoto T. Numerical verifications of solutions for nonlinear hyperbolic equations. Appl. Math. Lett. 10:(6):1997;91-96.
7. Plum M. Inclusion methods for elliptic boundary value problems. Studies in Computational Mathematics. 5:1994;323-379.