3 research outputs found
Optimal time delays in a class of reaction-diffusion equations
A class of semilinear parabolic reaction diffusion equations with multiple
time delays is considered. These time delays and corresponding weights are to
be optimized such that the associated solution of the delay equation is the
best approximation of a desired state function. The differentiability of the
mapping is proved that associates the solution of the delay equation to the
vector of weights and delays. Based on an adjoint calculus, first-order
necessary optimality conditions are derived. Numerical test examples show the
applicability of the concept of optimizing time delays.Comment: 17 pages, 2 figure