Variational stability and well-posedness in the optimal control of ordinary differential equations
Variational stability for generalized ordinary differential equations
Variétés inertielles dans le cas non auto-adjoint. Applications aux variétés lentes
Various half-eigenvalues of scalar -Laplacian with indefinite integrable weights.
Vector dissipativity theory for large-scale impulsive dynamical systems.
Vector fields and flows on differentiable stacks.
Vector fields generating more than one flow.
Vector fields, invariant varieties and linear systems
We investigate the interplay between invariant varieties of vector fields and the inflection locus of linear systems with respect to the vector field. Among the consequences of such investigation we obtain a computational criterion for the existence of rational first integrals of a given degree, bounds for the number of first integrals on families of vector fields, and a generalization of Darboux's criteria. We also provide a new proof of Gomez--Mont's result on foliations...
Vector fields, separatrices and Kato surfaces
We prove that a singular complex surface that admits a complete holomorphic vector field that has no invariant curve through a singular point of the surface is obtained from a Kato surface by contracting some divisor (in particular, it is compact). We also prove that, in a singular Stein surface endowed with a complete holomorphic vector field, a singular point of the surface where the zeros of the vector field do not accumulate is either a quasihomogeneous or a cyclic quotient singularity. We give...
Vector spaces over function fields. Vector spaces over analytic function fields being associated to ordinary differential equations.
Vector-valued modular forms associated to linear ordinary differential equations
We consider a class of linear ordinary differential equations determined by a modular form of weight one, and construct vector-valued modular forms of weight two by using solutions of such differential equations.
Verallgemeinerte gewöhnliche Differentialgleichungen; Systeme mit Impulsen auf Flächen. II
Verallgemeinerte gewöhnliche Differentialgleichungen; Systeme mit Impulsen auf Flächen. I
Verallgemeinerte Hill'sche Differentialgleichung
Verallgemeinerte lineare Differentialgleichungssysteme
Verallgemeinerungen eines Satzes von Leighton über die Oszillation selbstadjungierter Differentialgleichungen
Vergleichssatz für die Lösungen linearer Differential-Ungleichungen
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.