On long time integration of the heat equation (Q260131)

The author devises space-time variational formulations for the Fourier heat equation on the unbounded temporal interval \((0, \infty)\) using weighted Bochner spaces. A variational formulation of the heat equation is developed by the collocation method. Some examples are mentioned to illustrate that the discrete solutions converge exponentially with respect to the polynomial degree for sufficiently smooth data in the weighted space-time norm, but pointwise accuracy is not stablished for large times. Some theorems are stated and proved for isomorphisms.