| Autor: |
Wen Z; School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China. email:wenzj@lzu.edu.cn., Fan M, Asiri AM, Alzahrani EO, El-Dessoky MM, Kuang Y |
| Jazyk: |
angličtina |
| Zdroj: |
Mathematical biosciences and engineering : MBE [Math Biosci Eng] 2017 Apr 01; Vol. 14 (2), pp. 407-420. |
| DOI: |
10.3934/mbe.2017025 |
| Abstrakt: |
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. |
| Databáze: |
MEDLINE |
| Externí odkaz: |
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