Existence and incompressible limit of a tissue growth model with autophagy
Publication
, Journal Article
Liu, JG; Xu, X
Published in: SIAM Journal on Mathematical Analysis
January 1, 2021
In this paper we study a cross-diffusion system whose coefficient matrix is non-symmetric and degenerate. The system arises in the study of tissue growth with autophagy. The existence of a weak solution is established. We also investigate the limiting behavior of solutions as the pressure gets stiff. The so-called incompressible limit is a free boundary problem of Hele-Shaw type. Our key new discovery is that the usual energy estimate still holds as long as the time variable stays away from 0.
Duke Scholars
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Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2021
Volume
53
Issue
5
Start / End Page
5215 / 5242
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics
Citation
APA
Chicago
ICMJE
MLA
NLM
Liu, J. G., & Xu, X. (2021). Existence and incompressible limit of a tissue growth model with autophagy. SIAM Journal on Mathematical Analysis, 53(5), 5215–5242. https://doi.org/10.1137/21M1405253
Liu, J. G., and X. Xu. “Existence and incompressible limit of a tissue growth model with autophagy.” SIAM Journal on Mathematical Analysis 53, no. 5 (January 1, 2021): 5215–42. https://doi.org/10.1137/21M1405253.
Liu JG, Xu X. Existence and incompressible limit of a tissue growth model with autophagy. SIAM Journal on Mathematical Analysis. 2021 Jan 1;53(5):5215–42.
Liu, J. G., and X. Xu. “Existence and incompressible limit of a tissue growth model with autophagy.” SIAM Journal on Mathematical Analysis, vol. 53, no. 5, Jan. 2021, pp. 5215–42. Scopus, doi:10.1137/21M1405253.
Liu JG, Xu X. Existence and incompressible limit of a tissue growth model with autophagy. SIAM Journal on Mathematical Analysis. 2021 Jan 1;53(5):5215–5242.
Published In
SIAM Journal on Mathematical Analysis
DOI
EISSN
1095-7154
ISSN
0036-1410
Publication Date
January 1, 2021
Volume
53
Issue
5
Start / End Page
5215 / 5242
Related Subject Headings
- Applied Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics
- 0101 Pure Mathematics