DIFFUSION WAVE INITIATION PROBLEM FOR A NONLINEAR PARABOLIC SYSTEM IN THE CASES OF SPHERICAL AND CYLINDRICAL SYMMETRY

Abstract

Solutions having the form of a diffusion wave propagating in a medium at rest with a finite velocity to a nonlinear parabolic reaction–diffusion system are constructed and studied. A problem of initiating a diffusion wave by boundary conditions specified on a sphere (circular cylindrical surface) is considered in the cases of spherical and cylindrical symmetry for the first time. An existence and uniqueness theorem for a solution in the class of analytical functions is proven. An exact solution is constructed in the form of explicit formulas. A step-by-step iterative algorithm based on the collocation method and expansion in radial basis functions is proposed. Numerical calculations are performed, and their results are verified using the exact solution.