| In this short note we present an observability criterion for systems whose state is governed by a matrix Riccati di erential equation and whose output is given by an a ne transformation.

The following backward stochastic Riccati di erential equation (BSRDE in short) 8>>>>><>>>>>>>>>>>: dK = [AK +KA+ d X i=1 C 0 iKCi +Q+ d X i=1 (C 0 iLi + LiCi)

For xed = (x; t), we consider the solution u(f) to u (x; t) + Au(x; t) = f(x) (x; t); x 2 ; t > 0 u(x; 0) = u(x; 0) = 0; x 2 ; Bju(x; t) = 0; x 2 @ ; t > 0; 1 j m; where u = @u @t , u = @ u @t , R, r 1 is a bounded domain with smooth boundary, A is a uniformly symmetric elliptic di erential operator of order 2m with t-independent smooth coe cients, Bj , 1 j m, are t-independent boundary di eren...

Our goal in this paper is to use combined Laplace transform (CLT) and Adomian decomposition method(ADM) (that will be explained section 3), study approximate solutions for non-linear time-fractionalBurger's equation, fractional Burger's Kdv equation the modi?ed theCaputo Conformable derivatives. Comparison between two exact solution made.Here we report that method (LTDM) proved e?cient beused o...

A variety of in ltration techniques can be used to fabricate solid materials, particularly composites. In general these processes can be described with at least one time dependent partial di erential equation describing the evolution of the solid phase, coupled to one or more partial di erential equations describing mass transport through a porous structure. This paper presents a detailed mathe...

Multigrid can be formulated as an algorithm for an abstract problem that is independent of the partial di erential equation, domain, discretization method, and number of processors. In such an abstract setting, problems not arising from partial di erential equations can be treated also (c.f. aggregation-disaggregation methods). Quite general theory exists for linear problems, e.g., C. C. Dougla...

— We present necessary and su‰cient conditions to guarantee that at least one solution of an infinite dimensional stochastic di¤erential equation, which starts from a regular closed subset K of an Hilbert space, remains in K for all times.

After a series of application papers have proven the approach to be numerically e ective, this paper gives the rst theoretical foundation for methods solving partial di erential equations by collocation with (possibly radial) basis functions.

This paper studies the rst order necessary conditions for the optimal controls of semilinear and quasilinear parabolic partial di erential equations with pointwise state constraints. Pontryagin type maximum principle is obtained.

In this paper we describe how wavelets may be used to solve partial diierential equations. These problems are currently solved by techniques such as nite diierences, nite elements and multi-grid. The wavelet method, however, ooers several advantages over traditional methods. Wavelets have the ability to represent functions at diierent levels of resolution, thereby providing a logical means of d...