Local existence and uniqueness of regular solutions in a model of tissue invasion by solid tumours

Mathematical and Computer Modelling

Volumn 47, Issue 5-6, 2008, Pages 604-613

  Morales Rodrigo, Cristian ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Haptotaxis; Reaction diffusion equations; Tumour invasion of tissue; Uniqueness

Indexed keywords

CELLS; COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; TISSUE;

EXTRACELLULAR MATRIX; PROTEASES; REACTION DIFFUSION EQUATIONS; TISSUE INVASION; TUMOUR INVASION OF TISSUES;

ONCOGENIC VIRUSES;

EID: 38849157798     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2007.02.031     Document Type: Article

References (11)

1. Chaplain M.A.J., and Anderson A.R.A. Mathematical modelling of tissue invasion. In: Preziosi L. (Ed). Cancer Modelling and Simulation (2003), Chapman & Hall/CRT 269-297
2. Gajewski H., and Zacharias K. Global behaviour of a reaction-diffusion system modelling chemotaxis. Math. Nachr. 195 (1998) 77-114
3. Mantzaris N.V., Webb S., and Othmer H.G. Mathematical modelling of tumor-induced angiogenesis. J. Math. Biol. 49 (2004) 111-187
4. Perumpanani A.J., Norbury J., Sherratt J.A., and Byrne H.M. A two parameter family of travelling waves with a singular barrier arising from the modeling of matrix mediated malignant invasion. Physica D 126 (1999) 145-159
5. Marchant B.P., Norbury J., and Perumpanani A.J. Travelling shocks waves arising ia a model of malignant invasion. SIAM J. Appl. Math. 60 (2000) 463-476
6. Perumpanani A.J., and Byrne H.M. Extracellular matrix concentration exerts selection pressure on invasive cells. Eur. J. Cancer 35 (1999) 1274-1280
7. G. Lolas, Mathematical modelling of the urokinase plasminogen activation system and its role in cancer invasion of the tissue, Ph.D. Thesis, University of Dundee, 2003
8. Friedman A., and Tello J.I. Stability of solutions of chemotaxis equations in reinforced random walks. J. Math. Anal. Appl. 272 (2002) 138-163
9. Corrias L., Perthame B., and Zaag H. Global solutions of some chemotaxis and angiogenesis systems in high space dimensions. Milan J. Math. 72 (2004) 1-28
10. Biler P., Hebisch W., and Nadzieja T. The Debye system: Existence and large time behavior of solutions. Nonlinear Anal. TMA 23 (1994) 1189-1209
11. Ladyzenskaya O.A., Solonnikov V.A., and Ural'ceva N.N. Quasilinear equations of parabolic type. Translations of Mathematical Monographs vol. 23 (1968), AMS, Providence, RI