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In this paper, we discuss the evolution of the optical beam in nonlocal cubic nonlinear media, modeled by the nonlocal nonlinear Schrödinger equation (NNLSE). A different approximate model to the NNLSE is presented for the strongly nonlocal media with arbitrary response functions. An exact analytical solution of the model is obtained, and a spatial soliton(More)
This paper concerns continuous-time optimal investment and consumption decision of a CRRA investor who faces proportional transaction costs and finite time horizon. In the no consumption case, it has been studied by Liu and Loewenstein (2002) and Dai and Yi (2006). Mathematically, it is a singular stochastic control problem whose value function satisfies a(More)
The model of pricing American-style convertible bond is formulated as a zero-sum Dynkin game, which can be transformed into a parabolic variational inequality PVI . The fundamental variable in this model is the stock price of the firm which issued the bond, and the differential operator in PVI is linear. The optimal call and conversion strategies correspond(More)
This paper deals with the equation @1H…u† ‡ r‰~vH…u† ÿ ruŠ ˆ f in D0…XT †; where X is a bounded domain in R …n P 2† with @X 2 C; and XT ˆ X …0; T †: H is a maximal monotonic graph and ~v : XT ! R is a known smooth vector function. We prove the existence of weak solution, uniqueness and obtain an error estimate for the approximating process. Ó 1998 Elsevier(More)
In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat e goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space(More)