\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

On the Cauchy problem for differential-difference parabolic equations with high-order nonlocal terms of general kind

Abstract Related Papers Cited by
  • We study the Cauchy problem with bounded continuous initial-value functions for the differential-difference equation

    $\frac{\partial u}{\partial t}= \sum$nk,j,m=1$ a_{kjm}\frac{\partial^2u}{\partial x_k\partial x_j} (x_1,...,x_{m-1},x_m+h_{kjm},x_{m+1},...,x_n,t),$

    assuming that the operator on the right-hand side of the equation is strongly elliptic and the coefficients $a_{kjm}$ and $h_{kjm}$ are real. We prove that this Cauchy problem has a unique solution (in the sense of distributions) and this solution is classical in ${\mathbb R}^n \times (0,+\infty),$ find its integral representation, and construct a differential parabolic equation with constant coefficients such that the difference between its classical bounded solution satisfying the same initial-value function and the investigated solution of the differential-difference equation tends to zero as $t\to\infty$.

    Mathematics Subject Classification: Primary: 35K15, 35R10; Secondary: 35C15, 35B40.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
SHARE

Article Metrics

HTML views() PDF downloads(75) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return