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Volume 4, Issue 4
Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order

Zhou Yulin, Du Ming-sheng

J. Part. Diff. Eq.,4(1991),pp.21-40

Published online: 1991-04

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  • Abstract
The general difference schemes for the first boundary problem of the fully nonlinear parabolic systems of second order f(x, t, u, u_x, u_{xx}, u_t) = 0 are considered in the rectangular domain Q_T = {0 ≤ x ≤ l, 0 ≤ t ≤ T}, where u(x, t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m ≥ 1 for (x, t) ∈ Q_T and u, p, r, q ∈ R^m. The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a priori estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear parabolic systems are also obtained.
  • Keywords

Fully nonlinear parabolic system difference scheme stability convergence

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@Article{JPDE-4-21, author = {Zhou Yulin, Du Ming-sheng}, title = {Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {4}, pages = {21--40}, abstract = { The general difference schemes for the first boundary problem of the fully nonlinear parabolic systems of second order f(x, t, u, u_x, u_{xx}, u_t) = 0 are considered in the rectangular domain Q_T = {0 ≤ x ≤ l, 0 ≤ t ≤ T}, where u(x, t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m ≥ 1 for (x, t) ∈ Q_T and u, p, r, q ∈ R^m. The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a priori estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear parabolic systems are also obtained.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5781.html} }
TY - JOUR T1 - Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order AU - Zhou Yulin, Du Ming-sheng JO - Journal of Partial Differential Equations VL - 4 SP - 21 EP - 40 PY - 1991 DA - 1991/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5781.html KW - Fully nonlinear parabolic system KW - difference scheme KW - stability KW - convergence AB - The general difference schemes for the first boundary problem of the fully nonlinear parabolic systems of second order f(x, t, u, u_x, u_{xx}, u_t) = 0 are considered in the rectangular domain Q_T = {0 ≤ x ≤ l, 0 ≤ t ≤ T}, where u(x, t) and f(x, t, u, p, r, q) are two m-dimensional vector functions with m ≥ 1 for (x, t) ∈ Q_T and u, p, r, q ∈ R^m. The existence and the estimates of solutions for the finite difference system are established by the fixed point technique. The absolute and relative stability and convergence of difference schemes are justified by means of a series of a priori estimates. In the present study, the existence of unique smooth solution of the original problem is assumed. The similar results for nonlinear and quasilinear parabolic systems are also obtained.
Zhou Yulin, Du Ming-sheng. (1991). Difference Schemes of Fully Nonlinear Parabolic Systems of Second Order. Journal of Partial Differential Equations. 4 (4). 21-40. doi:
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