scholarly journals A viscosity solution method for the spreading speed formula in slowly varying media

2011 ◽  
Vol 60 (4) ◽  
pp. 1229-1248 ◽  
Author(s):  
Francois Hamel ◽  
Gregoire Nadin ◽  
Lionel Roques
Keyword(s):  
Viscosity Solution ◽  
Solution Method ◽  
Spreading Speed

scholarly journals Optimal Consumption in a Stochastic Ramsey Model with Cobb-Douglas Production Function

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Md. Azizul Baten ◽  
Anton Abdulbasah Kamil
Keyword(s):  
Production Function ◽  
Viscosity Solution ◽  
Solution Method ◽  
Hjb Equation ◽  
Optimal Consumption ◽  
Ramsey Model ◽  
Discounted Utility ◽  
Hamilton Jacobi Bellman Equation ◽  
Hamilton Jacobi Bellman ◽  
Douglas Production Function

A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity solution of the transformed Hamilton-Jacobi-Bellman equation associated with this model. Finally, the optimal consumption policy is derived from the optimality conditions in the HJB equation.

scholarly journals Invasive speed for a competition-diffusion system with three species

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chaohong Pan ◽  
Hongyong Wang ◽  
Chunhua Ou
Keyword(s):  
Solution Method ◽  
Lower Solution ◽  
Spreading Speed ◽  
Species Competition ◽  
Cooperative System ◽  
Competitive System ◽  
Volterra Type ◽  
Competitive Species ◽  
Multiple Species ◽  
Selection Of

<p style='text-indent:20px;'>Competition stems from the fact that resources are limited. When multiple competitive species are involved with spatial diffusion, the dynamics becomes even complex and challenging. In this paper, we investigate the invasive speed to a diffusive three species competition system of Lotka-Volterra type. We first show that multiple species share a common spreading speed when initial data are compactly supported. By transforming the competitive system into a cooperative system, the determinacy of the invasive speed is studied by the upper-lower solution method. In our work, for linearly predicting the invasive speed, we concentrate on finding upper solutions only, and don't care about the existence of lower solutions. Similarly, for nonlinear selection of the spreading speed, we focus only on the construction of lower solutions with fast decay rate. This greatly develops and simplifies the ideas of past references in this topic.</p>

Elasto-plastic state of curve beam system subjected to complex loading

1996 ◽  
Vol 18 (4) ◽  
pp. 14-22
Author(s):  
Vu Khac Bay
Keyword(s):  
Cylindrical Shell ◽  
Solution Method ◽  
Complex Loading ◽  
Numerical Results ◽  
Elastic Solution ◽  
Plastic State ◽  
Curve Beam ◽  
Elastic State ◽  
Elastic Plastic ◽  
Beam System

Investigation of the elastic state of curve beam system had been considered in [3]. In this paper the elastic-plastic state of curve beam system in the form of cylindrical shell is analyzed by the elastic solution method. Numerical results of the problem and conclusion are given.

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