scholarly journals Reaction-diffusion equations for interacting particle systems

1987 ◽  
Vol 47 (1-2) ◽  
pp. 293-293
Author(s):  
A. De Masi ◽  
P. A. Ferrari ◽  
J. L. Lebowitz
Keyword(s):  
Interacting Particle Systems ◽  
Reaction Diffusion ◽  
Particle Systems ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Interacting Particle

On three classical problems for Markov chains with continuous time parameters

1991 ◽  
Vol 28 (02) ◽  
pp. 305-320 ◽  
Author(s):  
Mu-Fa Chen
Keyword(s):  
Continuous Time ◽  
Transition Rate ◽  
Interacting Particle Systems ◽  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Particle Systems ◽  
Countable State Space ◽  
Interacting Particle ◽  
Countable State ◽  
Time Parameters

For a given transition rate, i.e., aQ-matrixQ= (qij) on a countable state space, the uniqueness of theQ-semigroupP(t) = (Pij(t)),the recurrence and the positive recurrence of the corresponding Markov chain are three fundamental and classical problems, treated in many textbooks. As an addition, this paper introduces some practical results motivated from the study of a type of interacting particle systems, reaction diffusion processes. The main results are theorems (1.11), (1.17) and (1.18). Their proofs are quite straightforward.

On three classical problems for Markov chains with continuous time parameters

1991 ◽  
Vol 28 (2) ◽  
pp. 305-320 ◽  
Author(s):  
Mu-Fa Chen
Keyword(s):  
Continuous Time ◽  
Transition Rate ◽  
Interacting Particle Systems ◽  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Particle Systems ◽  
Countable State Space ◽  
Interacting Particle ◽  
Countable State ◽  
Time Parameters

For a given transition rate, i.e., a Q-matrix Q = (qij) on a countable state space, the uniqueness of the Q-semigroup P(t) = (Pij(t)), the recurrence and the positive recurrence of the corresponding Markov chain are three fundamental and classical problems, treated in many textbooks. As an addition, this paper introduces some practical results motivated from the study of a type of interacting particle systems, reaction diffusion processes. The main results are theorems (1.11), (1.17) and (1.18). Their proofs are quite straightforward.

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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