Stability of Diffusion Coefficients in an Inverse Problem for the Lotka-Volterra Competition System

K. Sakthivel ^[1] ; N. Baranibalan ^[2] ; J.-H. Kim ^[1] ; K. Balachandran ^[2]
1. [1] Yonsei University
  
  Yonsei University
  
  Corea del Sur
2. [2] Bharathiar University
  
  Bharathiar University
  
  India
Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 111, Nº. 2, 2010, págs. 129-147
Idioma: inglés
DOI: 10.1007/s10440-009-9455-z
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Resumen
- First we establish a Carleman estimate for Lotka-Volterra competition-diffusion system of three equations with variable coefficients. Then the internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting of retrieving two smooth diffusion coefficients in the given parabolic system for the dimension n≤3. The proof of the results rely on Carleman estimates and certain energy estimates for parabolic system.