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On the expansion of solutions of Laplace-like equations into traces of separable higher dimensional functions. (arXiv:1807.05340v1 [math.NA])
来源于:arXiv
This paper deals with the equation $-\Delta u+\mu u=f$, $\mu$ a positive
constant, on high-dimensional spaces $\mathbb{R}^d$. If the right-hand side $f$
is a rapidly converging series of separable functions, the solution $u$ can be
represented in the same way. These constructions are based on the approximation
of the function $1/r$ by sums of exponential functions. We derive results of
related kind for more general right-hand sides $f(x)=F(Tx)$ that are
restrictions of separable functions $F$ on a higher dimensional space to a
linear subspace of arbitrary orientation. 查看全文>>
