In this paper we present a penalty method for solving a complementarity problem involving 2nd-order nonlinear parabolic differential operators. In this work we first rewrite the complementarity problem as a nonlinear variational inequality. Then, we define a nonlinear parabolic partial differential equation (PDE) approximating the variational inequality using a power penalty term with a penalty...

We construct and study a scalable overlapping Additive Schwarz-Richardson (ASR) algorithm for monotone nonlinear parabolic problems discretized implicitly in time. At each time step, the Additive Schwarz preconditioner is built using the linear part of the nonlinear operator, partitioning the domain of the problem into overlapping subdomains, solving local problems on these subdomains and solvi...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t A MATLAB-based one-way and two-way split-step parabolic equation software tool (PETOOL...

We characterize the price of a European option on several assets for a very risk-averse seller, in a market with small transaction costs as a solution of a nonlinear diffusion equation. This problem turns out to be one of asymptotic analysis of parabolic PDE, and the interesting feature is the role of a nonlinear PDE eigenvalue problem. In particular, we generalize previous work of Guy Barles a...

We consider a nonlinear backward heat conduction problem in a strip. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. We shall use a modified integral equation method to regularize the nonlinear problem. The error estimates of Hölder type of the regularized solutions are obtained. AMS subject classifications: 35K05, 35K99, 47J06, 4...

In 2002, J.M.Rassias (Uniqueness of quasi-regular solutions for bi-parabolic elliptic bi-hyperbolic Tricomi problem, Complex Variables, 47 (8) (2002), 707-718) imposed and investigated the biparabolic elliptic bi-hyperbolic mixed type partial differential equation of second order. In the present paper some boundary-value problems with non-local initial condition for model and degenerate parabol...

Two explicit error representation formulas are derived for degenerate parabolic PDEs, which are based on evaluating a parabolic residual in negative norms. The resulting upper bounds are valid for any numerical method, and rely on regularity properties of solutions of a dual parabolic problem in nondivergence form with vanishing diffusion coefficient. They are applied to a practical space-time ...

This paper introduces a method for synthesizing reduced-order nonlinear model-based predictive controllers that have support in an arbitrary open subset, for semilinear parabolic equations. The predictive control law is computed based on reduced-order, nonlinear multi-step-ahead finiteelement predictors, identified directly from experimental input-output data. An advantage of this approach is t...

In past decades, the optimal control of distributed parameter system had been received much more attention in academic field. A wide spectrum of problems in applications can be solved by methods of optimal control, such as chemical engineering and vehicle dynamics. Modern optimal control theories and applied models are not only represented by ODE, but also by PDE, especially nonlinear parabolic...

The global-in-time existence of nonnegative solutions to a parabolic strongly coupled system with mixed Dirichlet-Neumann boundary conditions is shown. The system describes the time evolution of the electron and hole densities in a semiconductor when electron-hole scattering is taken into account. The parabolic equations are coupled to the Poisson equation for the electrostatic potential. Writt...