Weak solution of semi-linear PDE, BSDE and homogenization

A Semi-Linear Elliptic PDE Model for the Static Solution of Josephson Junctions

In this study we derive a semi-linear Elliptic Partial Differential Equation (PDE) problem that models the static (zero voltage) behavior of a Josephson window jUllction. Iterative methods for solving this problem are proposed, analyzed and their convergence analysis is presented. The preliminary computational results that are given, show the modeling power of our approach and exhibit its compu...

semi-analytical solution for static and forced vibration problems of laminated beams through smooth fundamental functions method

در این پایان نامه روش جدیدی مبتنی بر روش حل معادلات دیفرانسیل پارهای بر اساس روش توابع پایه برای حل مسایل ارتعاش اجباری واستاتیک تیرها و صفحات لایه ای ارایه شده است که می توان تفاوت این روش با روش های متداول توابع پایه را در استفاده از توابع هموار در ارضاء معادلات حاکم و شرایط مرزی دانست. در روش ارایه شده در این پایاننامه از معادله تعادل به عنوان معادله حاکم بر رفتار سیستم استفاده شده است که مو...

BSDE Representation and Discretization for Hamilton-Jacobi-Bellman PDE

Weak hyper semi-quantales and weak hypervalued topological spaces

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued t...

Homogenization of semi-linear PDEs with discontinuous coefficients

We study the asymptotic behavior of the solution of semi-linear PDEs. Neither periodicity nor ergodicity assumptions are assumed. The coefficients admit only a limit in a C̀esaro sense. In such a case, the limit coefficients may have discontinuity. We use probabilistic approach based on weak convergence techniques for the associated backward stochastic differential equation in the S-topology. We...