A quasilinear parabolic problem is studied. By using the method of lines, the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown. Also given are L2 error estimates for the error between the extended fully discrete finite element solutions and the exact solution.
SIAM Journal of Numerical Analysis
Wei, Dongming, Existence, uniqueness, and numerical analysis of solutions of a quasilinear parabolic problem. SIAM J. Numer. Anal. 29 (1992), no. 2, 484–497.