CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

April 6, 2021 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

Rigorous FEM based forward in time integration of dissipative PDEs

Seminar presented by Piotr Kalita (Jagiellonian University, Poland)

We present the technique for computer assisted rigorous forward in time integration of problems governed by dissipative PDEs. The approach is based on the Finite Element Method. The key concepts lie in the propagation of the a priori energy estimates needed to bound the infinite dimensional remainder and in rigorous integration of differential inclusions. The technique is illustrated by the computer assisted construction of the time periodic solution for periodically forced one-dimensional Burgers equation with homogeneous Dirichlet boundary conditions. Talk is based on joint work with Piotr Zgliczyński.