scholarly journals A stability analysis for a semilinear parabolic partial differential equation

1974 ◽  
Vol 15 (3) ◽  
pp. 522-540 ◽  
Author(s):  
Nathaniel Chafee
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Stability Analysis ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Semilinear Parabolic

scholarly journals Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations

2018 ◽  
Vol 24 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Anthony Le Cavil ◽  
Nadia Oudjane ◽  
Francesco Russo
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Monte Carlo ◽  
Numerical Experiments ◽  
Type Equation ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Type Representation ◽  
Monte Carlo Algorithms ◽  
Semilinear Parabolic

Abstract The paper is devoted to the construction of a probabilistic particle algorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.

scholarly journals A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation

1996 ◽  
Vol 9 (4) ◽  
pp. 399-414 ◽  
Author(s):  
Jean-François Le Gall
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Probabilistic Approach ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Brownian Snake ◽  
Nonnegative Solutions ◽  
One To One ◽  
Dimension One ◽  
Semilinear Parabolic

We use the path-valued process called the “Brownian snake” to investigate the trace at the boundary of nonnegative solutions of a semilinear parabolic partial differential equation. In particular, we characterize possible traces and in dimension one we prove that nonnegative solutions are in one-to-one correspondence with their traces at the origin. We also provide probabilistic representations for various classes of solutions.This article is dedicated to the memory of Roland L. Dobrushin.

scholarly journals Time- or Space-Dependent Coefficient Recovery in Parabolic Partial Differential Equation for Sensor Array in the Biological Computing

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Guanglu Zhou ◽  
Boying Wu ◽  
Wen Ji ◽  
Seungmin Rho
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Iteration Method ◽  
Numerical Experiments ◽  
Sensor Array ◽  
Variational Iteration Method ◽  
Parabolic Partial Differential Equation ◽  
Partial Differential ◽  
Variational Iteration

This study presents numerical schemes for solving a parabolic partial differential equation with a time- or space-dependent coefficient subject to an extra measurement. Through the extra measurement, the inverse problem is transformed into an equivalent nonlinear equation which is much simpler to handle. By the variational iteration method, we obtain the exact solution and the unknown coefficients. The results of numerical experiments and stable experiments imply that the variational iteration method is very suitable to solve these inverse problems.

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