Abstract
The paper deals with quasilinear parabolic boundary value problems where the nonlinear coefficients and right-hand side are defined with respect to the unknown function u = u(x; t) only in a neighbourhood of the initial function. The quasilinear parabolic problem is approximated by linear elliptic problems by means of semidiscretization in time. Itis proved that the approximations converge uniformly although the data are not continuous functions, and the limit turns out to be the weak solution of the parabolic problem for sufficiently small time t . The crucial points of the paper are L_\infty -estimates to ensure that the approximations belong to the domain of non-linearities and uniform estimates of the discrete time derivatives in a Lebesgue space in order to obtain uniform convergence.
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
