Variational inclusions for a Sturm-Liouville type differential inclusion
We establish several variational inclusions for solutions of a nonconvex Sturm-Liouville type differential inclusion on a separable Banach space.
Variational method to the impulsive equation with Neumann boundary conditions.
Variational methods for boundary value problems.
Variational oscillation criteria for nonlinear nonhomogeneous differential equations.
Various half-eigenvalues of scalar -Laplacian with indefinite integrable weights.
Verallgemeinerte Hill'sche Differentialgleichung
Vergleichssätze für Komplexe Lineare Differentialgleichungen 2. Ordnung
Verification of functional a posteriori error estimates for obstacle problem in 2D
We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value...
Verification of functional a posteriori error estimates for obstacle problem in 1D
We verify functional a posteriori error estimate for obstacle problem proposed by Repin. Simplification into 1D allows for the construction of a nonlinear benchmark for which an exact solution of the obstacle problem can be derived. Quality of a numerical approximation obtained by the finite element method is compared with the exact solution and the error of approximation is bounded from above by a majorant error estimate. The sharpness of the majorant error estimate is discussed.
Volume Filling Effect in Modelling Chemotaxis
The oriented movement of biological cells or organisms in response to a chemical gradient is called chemotaxis. The most interesting situation related to self-organization phenomenon takes place when the cells detect and response to a chemical which is secreted by themselves. Since pioneering works of Patlak (1953) and Keller and Segel (1970) many particularized models have been proposed to describe the aggregation phase of this process. Most of...