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

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1. 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

2. 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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