Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model - Zijuan Wen; Meng Fan; Asim M. Asiri; Ebraheem O. Alzahrani; Mohamed M. El-Dessoky; Yang Kuang (Mathematical Biosciences and Engineering)
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, $ L^{p} $-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.