Produção Nacional
Numerical Control of a Semilinear Wave Equation on an Interval
2022; Springer International Publishing; Linguagem: Inglês
10.1007/978-3-030-94766-8_4
ISSN2197-117X
AutoresMarcelo Gusmão Paraíso Cavalcanti, Valéria Domingos Cavalcanti, Carole Rosier, Lionel Rosier,
Tópico(s)Numerical methods for differential equations
ResumoWe are concerned with the numerical exact controllability of the semilinear wave equation on the interval (0, 1). We introduce a Picard iterative scheme yielding a sequence of approximated solutions which converges towards a solution of the null controllability problem, provided that the initial data are small enough. The boundary control, which is applied at the endpoint $$x=1$$ , is taken in the space $$H^1_0(0,T)$$ for $$T=2$$ . For the linear part, the control input is obtained by imposing a transparent boundary condition at $$x=1$$ . Next, we provide several simulations to show the efficiency of the algorithm, using collocation pseudospectral methods on Chebychev grids to discretize the second order derivative in space in the wave equation.
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