for this workshop
Computer assisted proofs for stability analysis of nonlinear waves
American Institute of Mathematics, San Jose, California
Blake Barker, Emmanuel Fleurantin, and J.D. Mireles James
This workshop, sponsored by AIM and the NSF, will be devoted to solving open problems regarding the stability of nonlinear waves using computer assisted methods of proof. Some results using computer assisted methods of proof include Hilbert's 18th problem and Smale's 14th problem. Researchers have developed efficient methods for obtaining rigorous error bounds for numerical approximations of heteroclinic and homoclinic connections between fixed points in ODE systems. These rigorous computation methods establish the existence and uniqueness of the solution in addition to providing a tight, completely rigorous error bound. Thus, these rigorous computations can be used to prove Theorems. Similarly, researchers have developed efficient and robust numerical methods for computing quantities that relay information about the spectral stability of one-dimensional traveling wave solutions to PDEs, which in turn yields information regarding the nonlinear stability. This workshop will help researchers identify collaborative opportunities to use rigorous computation to prove theorems regarding open problems in nonlinear wave theory.
Because many of the tools used in studying the stability of one-dimensional waves do not apply in the multi-dimensional setting and because of the computational complexity of the multi-dimensional setting, computer assisted methods of proof may be an especially important resource in this setting. This workshop will bring researchers together to address the following topics:
- Computer assisted proofs for stability analysis of nonlinear waves.
- Stability of multi-dimensional non-planar traveling waves.
- Rigorous computation of center manifolds.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
The deadline to apply for support to participate in this workshop has passed.
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