Generalized Non-Homogeneous Morrey Spaces And Olsen Inequality

In this paper, we shall discuss some properties of generalized non-homogeneous Morrey spaces. In addition, we will also prove the Olsen inequality in the non-homogeneous setting. Our proof utilizes the result of (García-Cuerva and Martell, 2001) on the boundedness of the fractional integral operator on Lebesgue spaces of non-homogeneous type

Blow-Up Solution of Modified-Logistic-Diffusion Equation

Modified-Logistic-Diffusion Equation ut=Duxx+u|1-u| with Neumann boundary condition has a global solution, if the given initial condition ψ satisfies ψ(x)≤1, for all x∈[0,1]. Other initial conditions can lead to another type of solutions; i.e., an initial condition that satifies ∫01ψ(x)dx>1 will cause the solution to blow up in a finite time. Another initial condition will result in another kind of solution, which depends on the diffusion coefficient D. In this paper, we obtained the lower bound of D, so that the solution of Modified-Logistic-Diffusion Equation with a given initial condition will have a global solution

Pour un continuum de formation du secondaire au collégial : actes de la Journée pédagogique Secondaire-collégial du 5 octobre 2001

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