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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

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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