ﻻ يوجد ملخص باللغة العربية
Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a PDE model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A two-component system of predator-prey reaction-diffusion PDEs is used with spatially dependent parameters to benchmark the methods described. Applications to modelling the ecological habitat of marine plankton blooms by nonlinear data assimilation through remote sensing is discussed.
The physical world is governed by the laws of physics, often represented in form of nonlinear partial differential equations (PDEs). Unfortunately, solution of PDEs is non-trivial and often involves significant computational time. With recent develop
The work concerns a class of path-dependent McKean-Vlasov stochastic differential equations with unknown parameters. First, we prove the existence and uniqueness of these equations under non-Lipschitz conditions. Second, we construct maximum likeliho
Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stabili
We survey the theory of attractors of nonlinear Hamiltonian partial differential equations since its appearance in 1990. These are results on global attraction to stationary states, to solitons and to stationary orbits, on adiabatic effective dynamic
We propose a simple algebraic method for generating classes of traveling wave solutions for a variety of partial differential equations of current interest in nonlinear science. This procedure applies equally well to equations which may or may not be