Time-dependent singularities in the heat equation

Heat Equation and Reflected Brownian Motion in Time Dependent Domains

Numerical solution of time-dependent foam drainage equation (FDE)

Reduced Differental Transform Method (RDTM), which is one of the useful and effective numerical method, is applied to solve nonlinear time-dependent Foam Drainage Equation (FDE) with different initial conditions. We compare our method with the famous Adomian Decomposition and Laplace Decomposition Methods. The obtained results demonstrated that RDTM is a powerful tool for solving nonlinear part...

Controllability of the time discrete heat equation

Abstract. In this paper we study the controllability of an Euler Implicit time discrete heat equation in a bounded domain with a local internal controller. We prove that, based on Lebeau-Robbiano’s time iteration method, the projection in appropriate filtered space is null controllable with uniformly bounded control. In this way, the well-known null-controllability property of the heat equation...

The Heat Equation and Reflected Brownian Motion in Time-dependent Domains

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “non-cylindrical domains,” and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C-smooth time-dependent domains in the n-dimensional Euclidean space R. Various sample path properties of RBM, its two-sided transiti...

The Heat Equation and Reflected Brownian Motion in Time-dependent Domains by Krzysztof Burdzy,1

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as “noncylindrical domains,” and its connections with partial differential equations. Construction is given for RBM in C3-smooth time-dependent domains in the n-dimensional Euclidean space Rn. We present various sample path properties of the process, two-sided estimates for i...