On an inverse problem for a linear hyperbolic integrodifferential equation.
On analyticity of Ornstein-Uhlenbeck semigroups
Let be a transition semigroup of the Hilbert space-valued nonsymmetric Ornstein-Uhlenbeck process and let denote its Gaussian invariant measure. We show that the semigroup is analytic in if and only if its generator is variational. In particular, we show that the transition semigroup of a finite dimensional Ornstein-Uhlenbeck process is analytic if and only if the Wiener process is nondegenerate.
On Bernoulli decomposition of random variables and recent various applications
In this review, we first recall a recent Bernoulli decomposition of any given non trivial real random variable. While our main motivation is a proof of universal occurence of Anderson localization in continuum random Schrödinger operators, we review other applications like Sperner theory of antichains, anticoncentration bounds of some functions of random variables, as well as singularity of random matrices.
On Cauchy-Dirichlet problem in half-space for linear integro-differential equations in weighted Hölder spaces.
On changes of measure in stochastic volatility models.
On comparison principles for parabolic equations with nonlocal boundary conditions.
On contact problems for nonlinear parabolic functional differential equations.
On determination of two time-dependent coefficients in a parabolic equation.
On determining a riemannian manifold from the Dirichlet-to-Neumann map
On evolution equations for moving domains.
On evolution inequalities of a modified Navier-Stokes type. I
The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.
On exact solutions of one-dimensional diffusion problems with free boundaries for parabolic equations.
On existence and uniqueness of solutions of nonlocal problems for hyperbolic differential-functional equations in two independent variables
We seek for classical solutions to hyperbolic nonlinear partial differential-functional equations of the second order. We give two theorems on existence and uniqueness for problems with nonlocal conditions in bounded and unbounded domains.
On exponentially bounded solutions of linear parabolic difference-differential equations
On -differentiable Fredholm operators of nonstationary initial-boundary value problems
We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.
On FEM solution for 3D continuous casting problem
On first order impulsive semilinear functional differential inclusions
In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.
On Fractional Helmholtz Equations
MSC 2010: 26A33, 33E12, 33C60, 35R11In this paper we derive an analytic solution for the fractional Helmholtz equation in terms of the Mittag-Leffler function. The solutions to the fractional Poisson and the Laplace equations of the same kind are obtained, again represented by means of the Mittag-Leffler function. In all three cases the solutions are represented also in terms of Fox's H-function.
On functional linear partial differential equations in Gevrey spaces of holomorphic functions.
We investigate existence and unicity of global sectorial holomorphic solutions of functional linear partial differential equations in some Gevrey spaces. A version of the Cauchy-Kowalevskaya theorem for some linear partial -difference-differential equations is also presented.
On Gardings inequality.