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This article is cited in 5 scientific papers (total in 5 papers)
Asymptotics of the fundamental solution of a Petrovskii parabolic equation with constant coefficients
S. G. Gindikin, M. V. Fedoryuk
Abstract:
Let $P(\zeta)$, $\zeta\in\mathbf C^n$, be a homogeneous, parabolic polynomial of degree $2m$. Properties of the function
$$
\nu(\eta)=\min_{\xi\in\mathbf R^n}\operatorname{Re}P(\xi+i\eta),\qquad\eta\in\mathbf R^n,
$$
are investigated. Two-sided estimates are obtained for the fundamental solution $G(t,x)$ of the equation
$$
\frac{\partial u}{\partial t}+P\biggl(\frac1i\frac\partial{\partial x}\biggr)u=0,
$$
and an asymptotic decomposition is determined for $G(t,x)$ as $|x|^{2m}/t\to+\infty$ under the assumption that $\nu(\eta)\in C^1(\mathbf R^n)$.
Bibliography: 14 titles.
Received: 09.11.1972
Citation:
S. G. Gindikin, M. V. Fedoryuk, “Asymptotics of the fundamental solution of a Petrovskii parabolic equation with constant coefficients”, Mat. Sb. (N.S.), 91(133):4(8) (1973), 500–522; Math. USSR-Sb., 20:4 (1973), 519–542
Linking options:
https://www.mathnet.ru/eng/sm3313https://doi.org/10.1070/SM1973v020n04ABEH001889 https://www.mathnet.ru/eng/sm/v133/i4/p500
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Abstract page: | 417 | Russian version PDF: | 107 | English version PDF: | 13 | References: | 45 | First page: | 2 |
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