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math.AP2022
Finite-dimensional reduction of systems of nonlinear diffusion equations
A. V. Romanov
We present a class of one-dimensional systems of nonlinear parabolic equations for which long-time phase dynamics can be described by an ODE with a Lipschitz vector field in R^n. I…
math.AP2020
Final Dynamics of Systems of Nonlinear Parabolic Equations on the Circle
A. V. Romanov
We consider the class of dissipative reaction-diffusion-convection systems on the circle and obtain conditions under which the final (at large times) phase dynamics of a system can…