In this paper we first give a unified method by introducing the concept of admissible triplets to study local and global Cauchy problems for semi-linear parabolic equations with a general nonlinear term in different Sobolev spaces. In particular, we establish the local well-posedness and small global well-posedness of the Cauchy problem for semi-linear parabolic equations without the homogeneou...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...

We consider a backward parabolic partial differential equation with variable coefficient a(x, t) in time. A new modification is used on the logarithmic convexity method to obtain a conditional stability estimate. Based on a formal solution, we reveal the essence of the ill-posedness and propose a simple regularization method. Moreover, we apply the regularization method to two representative ca...

The paper investigates a contingent claim replicating problem for a diiusion market model. It is proposed an approach which does not call to solve the backward parabolic equation, unlike for the classical method, and this approach is applied for a case when the volatility coeecient is random and depends on time. The replicating strategy is decomposed to series of explicit strategies which does ...

A semilinear parabolic problem of second order with an unknown solely time-dependent convolution kernel is considered. An additional given global measurement (a space integral of the solution) ensures the existence of a unique weak solution. The unknown kernel function can be approximated by a time-discrete numerical scheme based on Backward Euler’s method (Rothe’s method). In this contribution...

This paper is addressed to establishing controllability and observability for some forward linear stochastic complex degenerate/singular Ginzburg-Landau equations. It sufficient establish appropriate inequalities the corresponding backward The key prove Carleman estimates of operators. Compared with existing deterministic results, it necessary overcome difficulties caused by coefficients random...

We study the relative value iteration for the ergodic control problem under a nearmonotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasi-linear parabolic Cauchy initial value problem in Rd. We show that this Cauchy problem stabilizes or, in other words, that the solution of the quasi-linear parabolic equation converge...

We propose in this paper a technique to accelerate the convergence of the Newton method to solve non-linear unsteady CFD problems. The principle relies on an effective way to obtain a better solution for the current time step than the solution of the previous time step. This is performed on a reduced model computed with a Proper Orthogonal Decomposition of some solution computed at some previou...

We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann–Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank...