distribution solution
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2019 ◽  
Vol 148 (11) ◽  
pp. 75-89
Author(s):  
Adrián Francisco Loera Castro ◽  
Alberto Ochoa Zezzatti ◽  
Jaime Sánchez ◽  
Humberto García Castellanos

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Shan Zheng ◽  
Zhengyong Ouyang ◽  
Kuilin Wu

AbstractIn this paper we study the Boussinesq equation with power law nonlinearity and dual dispersion which arises in fluid dynamics. A particular kind of product of distributions is introduced and applied to solve non-smooth solutions of this equation. It is proved that, under certain conditions, a distribution solution as a singular Dirac delta function exists for this model. For the first time, this kind of product of distributions is used to deal with a fourth order nonlinear partial differential equation.


2017 ◽  
Vol 22 (S5) ◽  
pp. 11069-11077
Author(s):  
Wei Zhang ◽  
Xinchang Zhang ◽  
Huiling Shi ◽  
Longquan Zhou

2015 ◽  
Vol 57 (2) ◽  
pp. 138-149
Author(s):  
B. VAN BRUNT ◽  
S. GUL ◽  
G. C. WAKE

We study a cell growth model with a division function that models cells which divide only after they have reached a certain minimum size. In contrast to the cases studied in the literature, the determination of the steady size distribution entails an eigenvalue that is not known explicitly, but is defined through a continuity condition. We show that there is a steady size distribution solution to this problem.


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