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1.
In this paper, solutions for two types of ultrametric kinetic equations of the form reaction-diffusion are obtained and properties
of these solutions are investigated. General method to find the solution of equation of the form
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
$
\tfrac{\partial }
{{\partial t}}f(x,t) = \int_{\mathbb{Q}_p } {W(|x - y|_p )(f(y,t) - f(x,t))dy + V(|x|_p )f(x,t),f(x,0) = \phi (|x|_p ),}
相似文献
2.
The scattering problem is studied, which is described by the equation (-Δ
x
+q(x,x/ɛ)−E)ψ = f(x), where ψ = ψ (x,ɛ) ∈ ℂ, x ℂ ℝ
d
, ɛ > 0, E > 0, the function q(x,y) is periodic with respect to y, and the function f is compactly supported. The solution satisfying radiation conditions at infinity is considered, and its asymptotic behavior
as ɛ → O is described. The asymptotic behavior of the scattering amplitude of a plane wave is also considered. It is shown
that in principal order both the solution and the scattering amplitude are described by the homogenized equation with potential
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