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991.
992.
Aboubakary Diakhaby 《随机分析与应用》2013,31(2):254-273
We study the homogenization of semilinear partial differential equations (PDEs) with nonlinear Neumann boundary condition, locally periodic coefficients, and highly oscillating drift and nonlinear term. Our method is entirely probabilistic, as in a periodic case by Ouknine and Pardoux [14] and builds on our earlier work [5], which gives us the locally periodic counterpart of Theorem 2.2 in Tanaka [21]. 相似文献
993.
We use Lévy random fields to model the term structure of forward default intensity, which allows to describe the contagion risks. We consider the pricing of credit derivatives, notably of defaultable bonds in our model. The main result is to prove the pricing kernel as the unique solution of a parabolic integro-differential equation by constructing a suitable contractible operator and then considering the limit case for an unbounded terminal condition. Finally, we illustrate the impact of contagious jump risks on the defaultable bond price by numerical examples. 相似文献
994.
995.
Abdelkader Boucherif Ali S. Al-Qahtani Bilal Chanane 《Numerical Functional Analysis & Optimization》2013,34(6):730-747
We discuss the propagation of heat along a homogeneous rod of length A under the influence of a nonlinear heat source and impulsive effects at fixed times. This problem is described by an initial-boundary value problem for a nonlinear parabolic partial differential equation subjected to impulsive effects at fixed times. Using Green's function, we convert the problem into a nonlinear integral equation. Sufficient conditions are provided that enable the application of fixed point theorems to prove existence and uniqueness of solutions. 相似文献
996.
In this article, the one-dimensional parabolic equation with three types of integral nonlocal boundary conditions is approximated by the implicit Euler finite difference scheme. Stability analysis is done in the maximum norm and it is proved that the radius of the stability region and the stiffness of the discrete scheme depends on the signs of coefficients in the nonlocal boundary condition. The known stability results are improved. In the case of a plain integral boundary condition, the conditional convergence rate is proved and the regularization relation between discrete time and space steps is proposed. The accuracy of the obtained estimates is illustrated by results of numerical experiments. 相似文献
997.
M. Marras 《Numerical Functional Analysis & Optimization》2013,34(4):453-468
We consider blow-up solutions to parabolic systems, coupled through their nonlinearities under various boundary conditions with nonlinearities depending on the gradient solution. To obtain a lower bound to blow up time t* for the vector solution, Sobolev-type inequalities are introduced to make use of a differential inequality technique. In addition for Dirichlet systems sufficient conditions are introduced to derive an upper bound for t* and to have a criterion for the global existence of the vector solution. 相似文献
998.
Jingtang Ma 《Numerical Functional Analysis & Optimization》2013,34(4):436-452
In this article, several cascading multilevel finite-element algorithms are considered to discretize nonlinear parabolic problems, of which the nonlinearity has either local or nonlocal form. Algorithm I solves only a stationary linear system of equations at each level of P1 finite element spaces, while Algorithm II works on the coupling of a stationary linear system of equations with a linear parabolic equation. The convergence orders of Algorithms I and II are both O(h J ) in the energy norm; in Algorithm I the estimation depends on the number of grids, while Algorithm II does not. Algorithm III is based on Picard linearization techniques and Algorithm IV on Newton iteration. Both algorithms have convergence order—O(h J ). 相似文献
999.
We derive new a priori error estimates for linear parabolic equations with discontinuous coefficients. Due to low global regularity of the solutions the error analysis of the standard finite element method for parabolic problems is difficult to adopt for parabolic interface problems. A finite element procedure is, therefore, proposed and analyzed in this paper. We are able to show that the standard energy technique of finite element method for non-interface parabolic problems can be extended to parabolic interface problems if we allow interface triangles to be curved triangles. Optimal pointwise-in-time error estimates in the L 2(Ω) and H 1(Ω) norms are shown to hold for the semidiscrete scheme. A fully discrete scheme based on backward Euler method is analyzed and pointwise-in-time error estimates are derived. The interfaces are assumed to be arbitrary shape but smooth for our purpose. 相似文献
1000.
《Analytical letters》2012,45(15):2931-2947
Abstract The physical-chemical regularities of aromatic compounds' effects in luciferase toxicity biotesting have been studied. The structures and physical-chemical characteristics of the toxicants and of the bioluminescent emitter were taken into account. The inhibition constants of bioluminescence intensiy (I) were calculated and interpreted from the viewpoint of the energy (electron) transfer processes. The induction period (P) and the increase of the time of the maximum light intensity (tM) which take place in the quinones' presence, have been shown to deal with hydrogen transfer processes. The values of I, P and tM have been shown to be connected with a size of the quinones' aromatic and aliphatic parts. P- and tM-dependencies on quinone's redox potential have been demonstrated. 相似文献