GLOBAL EXISTENCE AND UNIQUENESS OF CLASSICAL SOLUTIONS FOR A GENERALIZED QUASILINEAR PARABOLIC EQUATION WITH APPLICATION TO A GLIOBLASTOMA GROWTH MODEL

This paper studies the global existence and uniqueness of classicalsolutions for a generalized quasilinear parabolic equation withappropriate initial and mixed boundary conditions. Under somepracticable regularity criteria on diffusion item and nonlinearity, weestablish the local existence and uniqueness of classical solutionsbased on a contraction mapping. This local solution can be continuedfor all positive time by employing the methods of energy estimates, \begin{document}$ L^{p} $\end{document} -theory, and Schauder estimate of linear parabolic equations. Astraightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitroglioblastoma growth is also presented.