title: Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model.
abstract: This paper studies the global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with appropriate initial and mixed boundary conditions. Under some practicable regularity criteria on diffusion item and nonlinearity, we establish the local existence and uniqueness of classical solutions based on a contraction mapping. This local solution can be continued for all positive time by employing the methods of energy estimates, Lp-theory, and Schauder estimate of linear parabolic equations. A straightforward application of global existence result of classical solutions to a density-dependent diffusion model of in vitro glioblastoma growth is also presented.
authors.affiliation: School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China. email:wenzj@lzu.edu.cn.
authors.forename: Zijuan
authors.initials: Z
authors.lastname: Wen
authors.forename: Meng
authors.initials: M
authors.lastname: Fan
authors.forename: Asim M
authors.initials: AM
authors.lastname: Asiri
authors.forename: Ebraheem O
authors.initials: EO
authors.lastname: Alzahrani
authors.forename: Mohamed M
authors.initials: MM
authors.lastname: El-Dessoky
authors.forename: Yang
authors.initials: Y
authors.lastname: Kuang
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005909:Glioblastoma / Q000473:pathology*; D006801:Humans; D008954:Models, Biological