|Partial differential equations via new variational principles and convex analysis|
|Time：||16:30-17:30, 2017-5-12 (Fri.)|
|Instructor：||Abbas Momeni [Carleton University, Canada]|
|Place：||Lecture hall, Floor 3, Jin Chun Yuan West Building|
The object of this talk is to present new variational principles for certain differential equations.
These principles provide new representations and formulations for the superposition of the gradient of convex functions and symmetric operators.
They yield new variational resolutions for a large class of hamiltonian partial differential equations with variety of linear and nonlinear boundary conditions including many of the standard ones. This approach seems to offer several useful advantages: It associates to a boundary value problem several potential functions which can often be used with relative ease compared to other methods such as the use of Euler-Lagrange functions.
These potential functions are quite flexible, and can be adapted to easily deal with both nonlinear and homogeneous boundary value problems. Additionally, in some cases, this new method allows dealing with problems beyond the usual locally compactness structure (problems with a supercritical Sobolev nonlinearity).