"Application of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed reaction-diffusion equations with cubic nonlinearity"
Lukyanenko D.V. and Melnikova A.A.

The capabilities of asymptotic analysis methods for solving a coefficient inverse problem for a system of nonlinear singularly perturbed equations of reaction-diffusion type with cubic nonlinearity are shown. The problem considered for a system of partial differential equations is reduced to a system of algebraic equations that is much simpler for a numerical study and relates the data of the inverse problem (the information on the position of the reaction front in time) with the coefficient to be recovered. Numerical results confirm the efficiency of the proposed approach.

Keywords: singularly perturbed problem, interior and boundary layers, reaction-diffusion equation, inverse problem with the location of moving front data.

  • Lukyanenko D.V. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Ph.D., Associate Professor, e-mail: lukyanenko@physics.msu.ru
  • Melnikova A.A. – Lomonosov Moscow State University, Faculty of Physics; Leninskie Gory, Moscow, 119991, Russia; Ph.D., Assistant, e-mail: melnikova@physics.msu.ru