Numerical and analytical studies of a nonlinear parabolic equation with boundary conditions of a special form

The work deals with a one-dimensional nonlinear parabolic equation describing the processes of diffusion, filtration and heat conduction. Problems for three kinds of boundary conditions are studied. The analytical study is conducted with the use of solutions in the form of power series; corresponding theorems similar to the Cauchy–Kovalevskaya theorem are proved. Solution algorithms based on the boundary element method are constructed. Some examples are discussed.