Fujita exponents for a space–time weighted parabolic problem in bounded domains

2021 ◽  
Vol 62 ◽  
pp. 103358
Author(s):  
Xizheng Sun ◽  
Bingchen Liu ◽  
Fengjie Li
Keyword(s):  
Parabolic Problem ◽  
Space Time ◽  
Bounded Domains

scholarly journals Non-linear noise excitation for some space-time fractional stochastic equations in bounded domains

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Mohammud Foondun ◽  
Jebessa B. Mijena ◽  
Erkan Nane
Keyword(s):  
Stochastic Equations ◽  
Space Time ◽  
Bounded Domains ◽  
Non Linear

AbstractIn this paper we study non-linear noise excitation for the following class of space-time fractional stochastic equations in bounded domains:

scholarly journals Space–time fractional diffusion on bounded domains

2012 ◽  
Vol 393 (2) ◽  
pp. 479-488 ◽  
Author(s):  
Zhen-Qing Chen ◽  
Mark M. Meerschaert ◽  
Erkan Nane
Keyword(s):  
Fractional Diffusion ◽  
Space Time ◽  
Bounded Domains

scholarly journals PROBABILISTIC INTERPRETATION AND PARTICLE METHOD FOR VORTEX EQUATIONS WITH NEUMANN’S BOUNDARY CONDITION

2004 ◽  
Vol 47 (3) ◽  
pp. 597-624 ◽  
Author(s):  
Benjamin Jourdain ◽  
Sylvie Méléard
Keyword(s):  
Stokes Equations ◽  
Numerical Algorithms ◽  
Particle Method ◽  
Primary 60K35 ◽  
Space Time ◽  
Empirical Measure ◽  
Neumann Condition ◽  
Bounded Domains ◽  
Vortex Equation ◽  
Vortex Equations

AbstractWe are interested in proving the convergence of Monte Carlo approximations for vortex equations in bounded domains of $\mathbb{R}^2$ with Neumann’s condition on the boundary. This work is the first step towards justifying theoretically some numerical algorithms for Navier–Stokes equations in bounded domains with no-slip conditions.We prove that the vortex equation has a unique solution in an appropriate energy space and can be interpreted from a probabilistic point of view through a nonlinear reflected process with space-time random births on the boundary of the domain.Next, we approximate the solution $w$ of this vortex equation by the weighted empirical measure of interacting diffusive particles with normal reflecting boundary conditions and space-time random births on the boundary. The weights are related to the initial data and to the Neumann condition. We prove a trajectorial propagation-of-chaos result for these systems of interacting particles. We can deduce a simple stochastic particle algorithm to simulate $w$.AMS 2000 Mathematics subject classification: Primary 60K35; 76D05

scholarly journals Space-Time adaptive algorithm for the mixed parabolic problem

2006 ◽  
Vol 103 (3) ◽  
pp. 367-392 ◽  
Author(s):  
J. M. Cascón ◽  
L. Ferragut ◽  
M. I. Asensio
Keyword(s):  
Adaptive Algorithm ◽  
Parabolic Problem ◽  
Space Time

Superconvergence of the Space-Time Continuous Finite Elements with Interpolated Coefficients for Semilinear Parabolic Problems

2011 ◽  
Vol 314-316 ◽  
pp. 1670-1675 ◽  
Author(s):  
Zhi Guang Xiong ◽  
Guo Rong Chen ◽  
Xue Ling Wang
Keyword(s):  
Finite Element Method ◽  
Parabolic Problem ◽  
Linear Problem ◽  
Expansion Method ◽  
Space Time ◽  
Parabolic Problems ◽  
Orthogonal Expansion ◽  
Semilinear Parabolic ◽  
Global Error Estimates ◽  
Semilinear Parabolic Problem

In this article, a space-time continuous finite element method with interpolated coefficients for a class of semilinear parabolic problem is introduced and analyzed. Basic global error estimates are established under the convergence assumption for linear problem. Further application of the orthogonal expansion method which is to construct some superapproximate interpolating functions, the supperconvergence on mesh nodes is proved. Finally the result is tested by a numerical example.

Space, Time and Einstein

2002 ◽  
Author(s):  
J. B. Kennedy
Keyword(s):  
Space Time
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