Unstable patterns in reaction-diffusion model of early carcinogenesis
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Publication:390809
DOI10.1016/j.matpur.2012.09.011zbMath1295.35072arXiv1104.3592OpenAlexW2000898702MaRDI QIDQ390809
Anna Marciniak-Czochra, Grzegorz Karch, Kanako Suzuki
Publication date: 9 January 2014
Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1104.3592
Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Initial-boundary value problems for second-order parabolic systems (35K51) Pattern formations in context of PDEs (35B36)
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Cites Work
- Unnamed Item
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- Unnamed Item
- Global existence in reaction-diffusion systems with control of mass: a survey
- Global solutions of reaction-diffusion systems
- Dynamics of growth and signaling along linear and surface structures in very early tumors
- A density-dependent diffusion system with stable discontinuous stationary solutions
- Geometric theory of semilinear parabolic equations
- Mathematical biology. Vol. 2: Spatial models and biomedical applications.
- Reaction-Difusion Model of Early Carcinogenesis: The Effects of Influx of Mutated Cells
- Periodic solutions of 𝑥”+𝑐𝑥’+𝑔(𝑥)=𝜖𝑓(𝑡)
- Derivation of a Macroscopic Receptor-Based Model Using Homogenization Techniques
- Multiple Solutions of Two-Point Boundary Value Problems of Neumann Type with a Small Parameter
- The chemical basis of morphogenesis
- Strong two-scale convergence and corrector result for a receptor-based model of intercellular communication
- MODELLING OF EARLY LUNG CANCER PROGRESSION: INFLUENCE OF GROWTH FACTOR PRODUCTION AND COOPERATION BETWEEN PARTIALLY TRANSFORMED CELLS
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