EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 15 (2020) Math. Model. Nat. Phenom., 15 (2020) 66 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 15, 2020
Article Number 66
Number of page(s) 24
DOI https://doi.org/10.1051/mmnp/2020039
Published online 03 December 2020
  1. J. Alexander, R. Gardner and C.K.R.T. Jones, A topological invariant arising in the stability analysis of travelling waves. J. Reine Angew. Math. 410 (1990) 167–212. [Google Scholar]
  2. S. Cruz-García and C. García-Reimbert, On the spectral stability of standing waves of the one-dimensional M5-model. Discrete Contin. Dyn. Syst. B. 21 (2016) 1079–1099. [CrossRef] [Google Scholar]
  3. S. Cruz-García and C. García-Reimbert, Approximations and error bounds for traveling and standing wave solutions of the one-dimensional M5-model for mesenchymal motion. Bol. Soc. Mat. Mex. 26 (2020) 147–169. [CrossRef] [Google Scholar]
  4. M. Egeblad and Z. Werb, New functions for the matrix metalloproteinases in cancer progression. Nat. Rev. Cancer 2 (2002) 161–174. [CrossRef] [PubMed] [Google Scholar]
  5. G. Flores and R.G. Plaza, Stability of post-fertilization traveling waves. J. Differ. Equ. 247 (2009) 1529–1590. [CrossRef] [Google Scholar]
  6. P. Friedl and K. Wolf, Tumor cell invasion and migration: diversity and escape mechanisms. Nat. Rev. Cancer 3 (2003) 362–374. [CrossRef] [PubMed] [Google Scholar]
  7. J. Goodman, Nonlinear asymptotic stability of viscous shock profiles for conservation laws. Arch. Rational Mech. Anal. 95 (1986) 325–344. [CrossRef] [MathSciNet] [Google Scholar]
  8. J. Goodman, Remarks on the stability of viscous shock waves. In Viscous Profiles and Numerical Methods for Shock Waves, edited by M. Shearer. SIAM, Philadelphia, PA (1991) 66–72. [Google Scholar]
  9. T. Hillen, M5 mesoscopic and macroscopic models for mesenchymal motion. J. Math. Biol. 53 (2006) 585–616. [CrossRef] [PubMed] [Google Scholar]
  10. J. Humpherys and K. Zumbrun, An efficient shooting algorithm for Evans function calculations in large systems. Phys. D 220 (2006) 116–126. [CrossRef] [Google Scholar]
  11. J. Humpherys, On the shock wave spectrum for isentropic gas dynamics with capillarity. J. Differ. Equ. 246 (2009) 2938–2957. [CrossRef] [Google Scholar]
  12. H.-Y. Jin, J. Li and Z.-A. Wang, Asymptotic stability of traveling waves of a chemotaxis model with singular sensitivity. J. Differ. Equ. 255 (2013) 193–219. [CrossRef] [Google Scholar]
  13. T. Kapitula and K. Promislow, Spectral and Dynamical Stability of Nonlinear Waves. Springer, New York (2013). [CrossRef] [Google Scholar]
  14. J.A. McDonald and R.P. Mecham, Receptors for Extracellular Matrix. Academic Press, San Diego, California (1991). [Google Scholar]
  15. K.J. Palmer, Exponential dichotomies and transversal homoclinic points. J. Differ. Equ. 55 (1984) 225–256. [CrossRef] [Google Scholar]
  16. K.J. Palmer, Exponential dichotomies and Fredholm operators. Proc. Amer. Math. Soc. 104 (1988) 149–156. [CrossRef] [Google Scholar]
  17. J. Rottmann-Matthes, Linear stability of traveling waves in first-order hyperbolic PDEs. J. Dyn. Differ. Equ. 23 (2011) 365–393. [CrossRef] [MathSciNet] [Google Scholar]
  18. J. Rottmann-Matthes, Stability and freezing of nonlinear waves in first-order hyperbolic PDEs. J. Dyn. Differ. Equ. 24 (2012) 341–367. [CrossRef] [MathSciNet] [Google Scholar]
  19. B. Sandstede, Stability of travelling waves, In Handbook of Dynamical Systems. North-, Amsterdam (2002) 983–1055. [Google Scholar]
  20. D.H. Sattinger, On the stability of waves of nonlinear parabolic systems. Adv. Math. 22 (1976) 312–355. [CrossRef] [MathSciNet] [Google Scholar]
  21. Z.-A. Wang, T. Hillen and M. Li, Mesenchymal motion models in one dimension. SIAM J. Appl. Math. 69 (2008) 375–397. [CrossRef] [Google Scholar]
  22. K. Wolf, I. Mazo, H. Leung, K. Engelke, U.H. von Andrian, E.I. Deryugina, A.Y. Strongin, E.-B. Bröcker and P. Friedl, Compensation mechanism in tumor cell migration: mesenchymal-amoeboid transition after blocking of pericellular proteolysis. J. Cell Biol. 160 (2003) 267–277. [CrossRef] [PubMed] [Google Scholar]
  23. K. Zumbrun, Stability of large-amplitude shock waves of compressible Navier-Stokes equations, in Vol 3 of Handbook of Fluid Mechanics (2005) 311–533. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.