SIMULATION MODELLING OF SHALLOW WATER WAVES WITH RANDOM INITIAL DATA BASED ON THE BOUSSINESQ - LOVE EQUATION

Evgeniy Viktorovich Bychkov

Abstract


The paper proposes an algorithm for simulation modeling of damped shallow water waves based on the optimal control problem for solutions of an initial-boundary value problem for the Boussinesq--Love equation with random initial data. The mathematical model is based on the Boussinesq--Love equation with cubic nonlinearity and a Stokes-type damping term, homogeneous Dirichlet boundary conditions, and Showalter - Sidorov initial conditions. The initial data contain an additive normally distributed random variable. The model under study belongs to Sobolev-type models, since it is based on a degenerate equation. The proposed algorithm combines the phase space method, the Galerkin method, the Ritz method, and the differential evolution method.

Keywords


Boussinesq - Love equation; optimal control; second order semilinear Sobolev type equation; numirical method; simulation modelling

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References


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