Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their approximations

Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their... For a linearized finite-difference scheme approximating the Dirichlet problem for a multidimensional quasilinear parabolic equation with unbounded nonlinearity, we establish pointwise two-sided solution estimates consistent with similar estimates for the differential problem. These estimates are used to prove the convergence of finite-difference schemes in the grid L 2 norm. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Consistent two-sided estimates for the solutions of quasilinear parabolic equations and their approximations

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
D.O.I.
10.1134/S0012266117070126
Publisher site
See Article on Publisher Site

Abstract

For a linearized finite-difference scheme approximating the Dirichlet problem for a multidimensional quasilinear parabolic equation with unbounded nonlinearity, we establish pointwise two-sided solution estimates consistent with similar estimates for the differential problem. These estimates are used to prove the convergence of finite-difference schemes in the grid L 2 norm.

Journal

Differential EquationsSpringer Journals

Published: Aug 23, 2017

References

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