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Department of Mathematical Sciences University of Cincinnati Cincinnati, OH 45221-0025, USA

Department of Mathematical Sciences University of Cincinnati Cincinnati, OH 45221-0025, USA. Weiming Yu & Diego A. Murio. IPES 2003 Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa.

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Department of Mathematical Sciences University of Cincinnati Cincinnati, OH 45221-0025, USA

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  1. Department of Mathematical Sciences University of Cincinnati Cincinnati, OH 45221-0025, USA Weiming Yu & Diego A. Murio IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  2. 1. Lotka (1924) and Volterra (1926) established their original and famous predator-prey/competing species model 2.Theaim of the model is the quantification of the interaction within and between species and their environment IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  3. 3. The range of applications is pretty wide: ecological systems, conduction in nerves, epidemics, carbon monoxide poisoning, diffusion systems, chemical reactions, etc. 4. Modification of the equation IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  4. Inverse Problem: Given values of uat times T1 and T2, identify the coefficients a(x) and b(x) from the PDE problem IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  5. Solution: IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  6. Estimates: IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  7. Example: IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  8. Graph of the solution function u(x,t) IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  9. IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  10. a(x), epsilon = 0.010, 0.005 and 0.001 IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  11. b(x), epsilon = 0.010, 0.005 and 0.001 IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  12. Future Work: • Extension to higher dimensions • Extension to systems • Relation to IHCP IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  13. Brief References • Anthony W. Leung, Systems of Nonlinear Partial Differential Equations: Applications to Biology and Engineering, Kluwer Academic Publishers, 1989.  • D.A. Murio, C.E. Mejía and S. Zhan, ‘Discrete Mollification and Automatic Numerical Differentiation’, Computers Math. Applic. 35(5), 1-16, (1998). IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

  14. THANK YOU! IPES 2003Inverse Problems in Engineering Symposium The University of Alabama, Tuscaloosa

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