Optimizing the rate of decay of solutions of the wave equation using genetic algorithms: A counterexample to the constant damping conjecture

摘要

We consider the problem of optimizing the rate of decay of solutions of the linear damped wave equation on a bounded interval. This corresponds to optimizing the spectral abscissa of the associated linear operator. By writing the damping term as a Fourier cosine series and obtaining some inequalities that the coefficients in this series have to satisfy in order that the spectral abscissa be larger than a real number α, we are then able to use a genetic algorithm to obtain values of the spectral abscissa which are better than those given by the constant damping case. This provides a counterexample to the conjecture that the best possible decay was obtained for constant damping.