Rothe method for a mixed problem with an integral condition for the two-dimensional diffusion equation
The authors consider a two-dimensional heat equation in the unit square along with Neumann-type boundary conditions containing, on one side, an unknown function of \(t\). At the same time, the integral over the unit square of the solution is prescribed. The authors show that a related one-dimensional problem concerning the integral of the solution with respect to only one of the variables can be solved uniquely by the Rothe method, and they show stability and convergence results in corresponding function spaces.
scientific article; zbMATH DE number 2163622