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

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)407-420
Number of pages14
JournalMathematical Biosciences and Engineering
Volume14
Issue number2
DOIs
StatePublished - Apr 1 2017

Fingerprint

Quasilinear Parabolic Equations
Glioblastoma
Growth Model
Classical Solution
growth models
Global Existence
Existence and Uniqueness
Growth
Schauder Estimates
Regularity Criterion
Contraction Mapping
Mixed Boundary Conditions
Energy Estimates
Local Existence
Local Solution
Boundary conditions
Diffusion Model
Parabolic Equation
Existence Results
Linear equation

Keywords

  • Contraction map
  • Density-dependent diffusion
  • Glioblastoma growth model
  • Quasilinear parabolic equation
  • Regularity

ASJC Scopus subject areas

  • Medicine(all)
  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

Cite this

Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. / Wen, Zijuan; Fan, Meng; Asiri, Asim M.; Alzahrani, Ebraheem O.; El-Dessoky, Mohamed M.; Kuang, Yang.

In: Mathematical Biosciences and Engineering, Vol. 14, No. 2, 01.04.2017, p. 407-420.

Research output: Contribution to journalArticle

Wen, Zijuan ; Fan, Meng ; Asiri, Asim M. ; Alzahrani, Ebraheem O. ; El-Dessoky, Mohamed M. ; Kuang, Yang. / Global existence and uniqueness of classical solutions for a generalized quasilinear parabolic equation with application to a glioblastoma growth model. In: Mathematical Biosciences and Engineering. 2017 ; Vol. 14, No. 2. pp. 407-420.
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