In this paper we establish a geometric theory for abstract quasilinear parabolic equations. In particular, we study existence, uniqueness, and continuous dependence of solutions. Moreover, we give conditions for global existence and establish smoothness properties of solutions. The results are based on maximal regularity estimates in continuous interpolation spaces. An important new ingredient ...

in this paper we consider the european continuous installment call option. then  its linear complementarity formulation is given. writing the resulted problem in variational form, we prove the existence and uniqueness of its weak solution. finally finite element method is applied to price the european continuous installment call option.

We prove a general existence and uniqueness result of solutions for backward stochastic differential equation (BSDE) with Lipschitz condition. also establish continuous dependence property comparison theorem to this type BSDEs, thus strengthening existing results.

In this paper we study a system of stochastic differential equations with dissipative nonlinearity which arise in certain neurobiology models. Besides proving existence, uniqueness and continuous dependence on the initial datum, we shall be mainly concerned with the asymptotic behaviour of the solution. We prove the existence of an invariant ergodic measure ν associated with the transition semi...

Linear dynamically varying H∞ controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets. It is shown that the existence of a suboptimal H∞ controller is related to the existence of a bounded solution to a functional algebraic Riccati equation. Even though nonlinear systems running over compact sets could exhibit sensitive depende...

A survey on continuous, semidiscrete and discrete well-posedness and scale-space results for a class of nonlinear diiusion lters is presented. This class does not require any monotony assumption (comparison principle) and, thus, allows image restoration as well. The theoretical results include existence , uniqueness, continuous dependence on the initial image, maximum-minimum principles, averag...

Abstract In this work, we study the existence, uniqueness, and continuous dependence of solutions for a class fractional differential equations by using generalized Riesz operator. One can view results work as refinement existence theory with Riemann–Liouville, Caputo, classical derivative. Some special cases be derived to obtain corresponding equations. We provide an illustrated example unique...