On existence and nonexistence results for nonlinear Schrödinger equations
On iterative solution of nonlinear heat-conduction and diffusion problems
The present paper deals with the numerical solution of the nonlinear heat equation. An iterative method is suggested in which the iterations are obtained by solving linear heat equation. The convergence of the method is proved under very natural conditions on given input data of the original problem. Further, questions of convergence of the Galerkin method applied to the original equation as well as to the linear equations in the above mentioned iterative method are studied.
An application of eigenfunctions of -Laplacians to domain separation
We are interested in algorithms for constructing surfaces of possibly small measure that separate a given domain into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the -Laplacians, , under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.
On uniqueness and stability of steady-state carrier distributions in semiconductors
On an initial-boundary value problem for the nonlinear Schrödinger equation.
On an initial-value problem for a nonlinear transport equation in polymer chemistry
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