Dynamic Optimization of Dissipative PDE Systems Using Approximate Inertial Manifolds
نویسندگان
چکیده
Abstract In this work, we propose a computationally efficient method for the solution of dynamic constraint optimization problems arising in the context of spatiallydistributed processes governed by highly-dissipative nonlinear partial differential equations (PDEs). The method is based on spatial discretization using combination of the method of weighted residuals with spatially-global basis functions and approximate inertial manifolds. We use the Kuramoto-Sivashinsky equation, a model of wavy behavior, to demonstrate the implementation and evaluate the effectiveness of the proposed optimization method.
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