unbounded spatial domains
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Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 286
Author(s):  
Michael Marcozzi

We demonstrate the existence, uniqueness and Galerkin approximatation of linear ultraparabolic terminal value/infinite-horizon problems on unbounded spatial domains. Furthermore, we provide a probabilistic interpretation of the solution in terms of the expectation of an associated ultradiffusion process.





2013 ◽  
Vol 3 (4) ◽  
pp. 283-292 ◽  
Author(s):  
Man Luo ◽  
Da Xu ◽  
Limei Li

AbstractThe numerical solution of a parabolic Volterra integro-differential equation with a memory term on a one-dimensional unbounded spatial domain is considered. A quasi-wavelet based numerical method is proposed to handle the spatial discretisation, the Crank-Nicolson scheme is used for the time discretisation, and second-order quadrature to approximate the integral term. Some numerical examples are presented to illustrate the efficiency and accuracy of this approach.



2013 ◽  
Vol 24 (4) ◽  
pp. 471-500 ◽  
Author(s):  
M. AL-JARARHA ◽  
CHUNHUA OU

In this paper we investigate the population dynamics of a species with age structure in the case where the diffusion and death rates of the matured population are both age-dependent. We develop a new application of the age-structure technique in terms of an integral equation. For unbounded spatial domains, we study the existence of travelling waves, whilst in bounded domains, we investigate the existence of positive steady-state solutions and their stability.



2005 ◽  
Vol 55 (1) ◽  
pp. 83-99 ◽  
Author(s):  
Houde Han ◽  
Liang Zhu ◽  
Hermann Brunner ◽  
Jingtang Ma


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