ADVECTION-DIFFUSION MODELS FOR SOLID TUMOUR EVOLUTION IN VIVO AND RELATED FREE BOUNDARY PROBLEM
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Publication:4798799
DOI10.1142/S0218202500000239zbMath1008.92017OpenAlexW2039827595MaRDI QIDQ4798799
Luigi Preziosi, Elena De Angelis
Publication date: 16 March 2003
Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s0218202500000239
Probabilistic models, generic numerical methods in probability and statistics (65C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Free boundary problems for PDEs (35R35)
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Cites Work
- A new approach to modelling the formation of necrotic regions in tumours
- Mathematical models for tumour angiogenesis: Numerical simulations and nonlinear wave solutions
- The effect of time delays on the dynamics of avascular tumor growth
- Modelling the role of cell-cell adhesion in the growth and development of carcinomas
- The role of growth factors in avascular tumour growth
- A mathematical analysis of a model for tumour angiogenesis
- A mathematical model of vascular tumour growth and invasion
- Necrosis and Apoptosis: Distinct Cell Loss Mechanisms in a Mathematical Model of Avascular Tumour Growth
- STRATEGIES OF APPLIED MATHEMATICS TOWARDS AN IMMUNO-MATHEMATICAL THEORY ON TUMORS AND IMMUNE SYSTEM INTERACTIONS
- Free boundary value problems associated with the growth and development of multicellular spheroids
- MATHEMATICAL MODELLING OF MACROPHAGE DYNAMICS IN TUMOURS
- A COMPARISON OF THE ROLES OF LOCALISED AND NONLOCALISED GROWTH FACTORS IN SOLID TUMOUR GROWTH
- AVASCULAR TUMOUR DYNAMICS AND NECROSIS
- POST-SURGICAL PASSIVE RESPONSE OF LOCAL ENVIRONMENT TO PRIMARY TUMOR REMOVAL II: HETEROGENEOUS MODEL
