In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted -spaces.
In this paper we consider the problem of detecting pollution in some non linear parabolic systems using the sentinel method. For this purpose we develop and analyze a new approach to the discretization which pays careful attention to the stability of the solution. To illustrate convergence properties we give some numerical results that present good properties and show new ways for building discrete sentinels.
We discuss the formulation of a simulator in three spatial dimensions for a multicomponent, two phase (air, water) system of groundwater flow and transport with biodegradation kinetics and wells with multiple screens. The simulator has been developed for parallel, distributed memory, message passing machines. The numerical procedures employed are a fully implicit expanded mixed finite element method for flow and either a characteristics-mixed method or a Godunov method for transport and reactions...
We give a derivation of an a-posteriori strategy for choosing the regularization parameter in Tikhonov regularization for solving nonlinear ill-posed problems, which leads to optimal convergence rates. This strategy requires a special stability estimate for the regularized solutions. A new proof fot this stability estimate is given.
In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions and .
We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.
We consider a phase-field model of grain structure evolution, which appears in materials sciences. In this paper we study the grain boundary motion model of Kobayashi-Warren-Carter type, which contains a singular diffusivity. The main objective of this paper is to show the existence of solutions in a generalized sense. Moreover, we show the uniqueness of solutions for the model in one-dimensional space.
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22The fractional calculus (FC) is an area of intensive research and development. In a previous paper and poster we tried to exhibit its recent state, surveying the period of 1966-2010. The poster accompanying the present note illustrates the major contributions during the period 1695-1970, the "old history" of FC.
MSC 2010: 26A33, 05C72, 33E12, 34A08, 34K37, 35R11, 60G22In the last decades fractional calculus became an area of intense re-search and development. The accompanying poster illustrates the major contributions during the period 1966-2010.
Mathematical models for option pricing often result in partial differential equations. Recent enhancements are models driven by Lévy processes, which lead to a partial differential equation with an additional integral term. In the context of model calibration, these partial integro differential equations need to be solved quite frequently. To reduce the computational cost the implementation of a reduced order model has shown to be very successful numerically. In this paper we give a priori error...