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Search: All articles in the CMB digital archive with keyword Diffusion

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1. CMB Online first

Liu, Li; Weng, Peixuan
Globally asymptotic stability of a delayed integro-differential equation with nonlocal diffusion
We study a population model with nonlocal diffusion, which is a delayed integro-differential equation with double nonlinearity and two integrable kernels. By comparison method and analytical technique, we obtain globally asymptotic stability of the zero solution and the positive equilibrium. The results obtained reveal that the globally asymptotic stability only depends on the property of nonlinearity. As application, an example for a population model with age structure is discussed at the end of the article.

Keywords:integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure
Categories:45J05, 35K57, 92D25

2. CMB 2011 (vol 55 pp. 623)

Pan, Jiaqing
The Continuous Dependence on the Nonlinearities of Solutions of Fast Diffusion Equations
In this paper, we consider the Cauchy problem $$ \begin{cases} u_{t}=\Delta(u^{m}), &x\in{}\mathbb{R}^{N}, t>0, N\geq3, \\ % ^^----- here u(x,0)=u_{0}(x), &x\in{}\mathbb{R}^{N}. \end{cases} $$ We will prove that: (i) for $m_{c}
Keywords:fast diffusion equations, Cauchy problem, continuous dependence on nonlinearity
Categories:35K05, 35K10, 35K15

3. CMB 2011 (vol 55 pp. 3)

Agarwal, Ravi P.; Mustafa, Octavian G.
On a Local Theory of Asymptotic Integration for Nonlinear Differential Equations
We improve several recent results in the asymptotic integration theory of nonlinear ordinary differential equations via a variant of the method devised by J. K. Hale and N. Onuchic The results are used for investigating the existence of positive solutions to certain reaction-diffusion equations.

Keywords:asymptotic integration, Emden-Fowler differential equation, reaction-diffusion equation
Categories:34E10, 34C10, 35Q35

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