会议介绍

Majority of phenomena in science and engineering can be mathematically described by either linear or nonlinear, often partial differential equation (PDE) models. As the solutions to the underlying application problems largely depend on the solutions to their mathematical models, solving these PDE models has been critically important for the resolutions of these scientific and engineering problems. As the field of numerical methods for linear PDEs has become mature, the focus of research have been shifted and devoted to developing efficient numerical methods for nonlinear PDEs, in particular, for strongly nonlinear PDEs. Such nonlinear PDEs arise not only from sub-fields within mathematics such as differential geometry and analysis but also from many scientific and engineering fields such as astrophysics, cosmology, fluid dynamics, geo-science, general relativity, image processing, materials science, mathematical finance, medical science, optimal control, quantum mechanics, system biology. They are often at the heart of the overall procedure of solving the underlying application problems, as rightfully noted by the renowned physicist and Nobel laureate Werner Heisenberg: ``.... the progress of physics will to a large extent depend on the progress of nonlinear mathematics, of methods to solve nonlinear equations.... and therefore we can learn by comparing different nonlinear problems." Despite its importance in sciences, the study for numerical methods in nonlinear problems is far from mature. There is an urgent need for communication between different disciplines for nonlinear problems including pure mathematicians, engineers, as well as numerical analysts.

The workshop aims at bringing together researchers and scientists including post-docs and graduate students to exchange and stimulate ideas in numerical solutions for nonlinear problems, with a special focus on novel approaches and new directions for nonlinear PDEs. Techniques from a number of research areas including geometry, machine learning, non-local calculus, partial differential equation theory and numeric would make this workshop a real inter-disciplinary one with promising industrial applications. For this workshop, we will put emphasis to include techniques related to: 1) recent development in theory for nonlinear PDEs, 2) nonlinear calculus, 3) cutting-edge numerical techniques in solving nonlinear problems.

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