scholarly journals Derivation of stochastic partial differential equations for size- and age-structured populations

2009 ◽  
Vol 3 (1) ◽  
pp. 73-86 ◽  
Author(s):  
Edward J. Allen
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Structured Populations ◽  
Partial Differential ◽  
Age Structured

Stability for a competing system of hierarchical age-structured populations

2020 ◽  
Vol 13 (07) ◽  
pp. 2050070
Author(s):  
Ze-Rong He ◽  
Nan Zhou
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Experiments ◽  
Structured Populations ◽  
Vital Rates ◽  
Partial Differential ◽  
Semigroup Method ◽  
Age Structured ◽  
The Stability

In this paper, we are concerned with the stability for a model in the form of system of integro-partial differential equations, which governs the evolution of two competing age-structured populations. The age-specified environment is incorporated in the vital rates, which displays the hierarchy of ages. By a non-zero fixed-point result, we show the existence of positive equilibria. Some conditions for the stability of steady states are derived by means of semigroup method. Furthermore, numerical experiments are also presented.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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