On the Chaplyghin method for generalized solutions of partial differential functional equations.
On the controllability of fractional dynamical systems
This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder's fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.
On the convergence of gelerkin approximations
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial chaos expansions to the correct limit and complement...
On the convergence of generalized polynomial chaos expansions
A number of approaches for discretizing partial differential equations with random data are based on generalized polynomial chaos expansions of random variables. These constitute generalizations of the polynomial chaos expansions introduced by Norbert Wiener to expansions in polynomials orthogonal with respect to non-Gaussian probability measures. We present conditions on such measures which imply mean-square convergence of generalized polynomial...
On the Convergence of the Approximate Free Boundary for the Parabolic Obstacle Problem
Si discretizza il problema dell'ostacolo parabolico con differenze all'indietro nel tempo ed elementi finiti lineari nello spazio e si dimostrano stime dell'errore per la frontiera libera discreta.
On the convergence of the stochastic Galerkin method for random elliptic partial differential equations
In this article we consider elliptic partial differential equations with random coefficients and/or random forcing terms. In the current treatment of such problems by stochastic Galerkin methods it is standard to assume that the random diffusion coefficient is bounded by positive deterministic constants or modeled as lognormal random field. In contrast, we make the significantly weaker assumption that the non-negative random coefficients can be bounded strictly away from zero and infinity by random...
On the distributional solution of the inverse problem induced by the heat kernel method.
On the domain dependence of solutions to the two-phase Stefan problem
We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains converge to a solution of the same problem on a domain where is the limit of in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on .
On the evolution equations of viscous gaseous stars
On the exact controllability of a nonlinear stochastic heat equation.
On the existence and uniqueness of solutions of the Goursat problem for systems of functional partial differential equations of hyperbolic type.
On the existence of classical solutions for differential-functional IBVP.
On the existence of generalized solutions of nonlinear first order partial differential-functional equations in two independent variables
On the existence of shock propagation in a flow through deformable porous media
We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution in the case of onset of singularities, which can be interpreted as a local collapse of the medium, in the general...
On the existence of solutions of nonlinear infinite systems of parabolic differential-functional equations.
On the existence of solutions of the Darboux problem for the hyperbolic partial differential equations in Banach spaces
On the existence of weak solutions of boundary value problems in a diffusion model for an inhomogeneous liquid in regions with moving boundaries
On the fractional differentiability of the spatial derivatives of weak solutions to nonlinear parabolic systems of higher order
We are concerned with the problem of differentiability of the derivatives of order of solutions to the “nonlinear basic systems” of the type We are able to show that for and this result suggests that more regularity is not expectable.
On the global existence theorem for a free boundary problem for equations of a viscous compressible heat conducting capillary fluid.