|Applied PDEs: Analysis and Computation|
|Time：||Wed. 13:00-14:50; Fri. 8:00-9:50|
|Instructor：||Hailiang Liu [Iowa State University]|
|Place：||Conference room 3 , Floor 2, Jin Chun Yuan West Building|
This course will provide students with basic techniques for doing a priori estimates of solutions to some significant time dependent partial differential equations (PDEs). Such estimates, showing how solutions depend on the given data (initial data and/or boundary data), are of fundamental importance in both development of theory of PDEs and construction of numerical approximations of their solutions. Analytic tools to be introduced include Methods of invariant region; Energy methods; Entropy methods; and critical threshold dynamics. Examples of applications are such as reaction-diffusion equations in population dynamics, Navier-Stokes equations in fluid dynamics; kinetic equations in particle dynamics, and Euler-Possion equations in plasma dynamics.
The short course starts with an overview of some fundamental PDEs and their applications, with main focus on the solution estimates, evolving along with a good balance between physics behind, the intrinsic mathematical structure and the associated computational aspects. A course is suitable for students in applied mathematics whose primary interest is in analysis of PDEs and/or design of numerical algorithms for computing scientific problems.
Knowledge in partial differential equations.
Reference for the course:
References for research articles will be given during the course.