Determination of initial data for a reaction-diffusion system with variable coefficients

Vo Van Au, Mokhtar Kirane, Nguyen Huy Tuan

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this paper, we study a final value problem for a reaction-diffusion system with time and space dependent diffusion coefficients. In general, the inverse problem of identifying the initial data is not well-posed, and herein the Hadamard-instability occurs. Applying a new version of a modified quasi-reversibility method, we propose a stable approximate (regularized) problem. The existence, uniqueness and stability of the corresponding regularized problem are obtained. Furthermore, we also investigate the error estimate and show that the approximate solution converges to the exact solution in L2 and H0 1 norms. Our method can be applied to some concrete models that arise in biology, chemical engineering, etc.

Original languageBritish English
Pages (from-to)771-801
Number of pages31
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume39
Issue number2
DOIs
StatePublished - Feb 2019

Keywords

  • Backward problem
  • Ill-posed problem
  • Quasi-reversibility method
  • Reaction-diffusion system
  • Regularization

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