In recent years, many authors have investigated the blow-up phenomenon of reaction-diffusion equations with nonlocal source terms or localized source terms subject to Neumann boundary conditions.
This article deals with the porous medium equation with local and localized source terms, represented by two factors v q 1 ( x, τ ) and v s 1 ( 0, τ ), respectively.
Since many of the acceleration and loss processes of the high-energy electrons are expected to be localized in terms of the local time (e.g., Summers et al. 1998; Ukhorskiy et al. 2009), it is important to assess effects of each process by simultaneous observations at different locations in geospace.
In the case of spatially localized source terms, the decomposition allows severe truncation of the resulting algebraic system.
We present a new method for solving two-dimensional convection-dominated convection-diffusion equations containing spatially and temporally localized source terms.
Only, since gravitational energy can not be localized in terms of an energy density tensor, but is possessed by the field holistically, neither can this mass be localized.
The teleological also remains important in their thought, but it is reduced in scale from the world historical and localized in terms of anticipatory experiences and goal oriented activities.
"We're responding to user demand by creating a community that is localized in terms of language and culture, while connecting members to the rest of MySpace's global network".
Wang and Wang [17] considered the nonlocal equation begin{aligned} u_{t}-Delta u=int_{Omega}f bigl u t,x bigr),dx,quad xinOmega, t>0, end{aligned} (1.5) and Chadam et al. [18] considered the equation with a localized source term begin{aligned} u_{t}-Delta u=fbigl u t,x_{0} bigr), quad x_{0}, xinOmega, t>0, end{aligned} (1.6) with homogeneous Neumann boundary values and nonnegative initial data.
