UDC 519.6
MATHEMATICAL MODELING OF QUADRATICALLY NONLINEAR
SPATIALLY DISTRIBUTED SYSTEMS.
I. THE CASE OF CONTINUOUSLY DEFINED INITIAL-BOUNDARY
EXTERNAL-DYNAMIC DISTURBANCES
Abstract. Two classes of nonlinear spatially distributed dynamical systems, discretely observed according to the initial-boundary
and spatially distributed external-dynamic disturbances are analyzed. For each of them, analytical dependences are constructed
for the state function, which agrees, according to the root-mean square criterion, with the available information on the external-dynamic
conditions of their operation. Solution of the initial-boundary-value problems for the systems under study is defined in terms of a set of vectors,
which, according to the root-mean square criterion, model the given initial-boundary environment, including the spatially distributed external-dynamic
perturbations. Conditions of the accuracy and uniqueness of the obtained mathematical results are presented.
The cases of unbounded spatial dmains and systems’ steady-state dynamics are considered.
Keywords: pseudosolutions, mathematical modeling of dynamic systems, spatially distributed dynamical systems,
systems with uncertainties, ill-posed initial-boundary-value problems.
FULL TEXT
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