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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Unlike the mass and center of mass, the variance,or ”time-shift,” of a solution is not a conserved quantity for the non linear problem
📌 3 Key Takeaways
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Objective & Hypothesis:We show that the long time asymptotic solutions of initial value problems for linear and nonlinear mathematical models of tumor angiogenesisare self-similar spreading solutions.
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Key Findings & Data:The symmetries of the governing equationsyield three-parameter families of these solutions given in terms of their mass,center of mass, and variance.
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Conclusion & Impact:Unlike the mass and center of mass, the variance,or ”time-shift,” of a solution is not a conserved quantity for the non linear problem
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Asymptotic solutions · governing equation · nonlinear problem
Abstract
We show that the long time asymptotic solutions of initial value problems for linear and nonlinear mathematical models of tumor angiogenesisare self-similar spreading solutions. The symmetries of the governing equationsyield three-parameter families of these solutions given in terms of their mass,center of mass, and variance. Unlike the mass and center of mass, the variance,or ”time-shift,” of a solution is not a conserved quantity for the non linear problem
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Cite This Article
PAMUK, S., ATAC, İ. (2014). SELF-SIMILAR ASYMPTOTICS FOR LINEAR AND NONLINEAR MATHEMATICAL MODELS OF TUMOR ANGIOGENESIS: A REVIEW. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 63 - Sayı: 2, 71–79. https://ajindex.com/articles/747365