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 Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 6, Pages 1312–1330 (Mi izv975)

Parabolic equations over the field of $p$-adic numbers

A. N. Kochubei

Abstract: The author constructs and investigates a fundamental solution of Cauchy's problem for a parabolic equation with a $p$-adic space variable and a real time variable. The question of existence and uniqueness of solutions to Cauchy's problem in classes of bounded and increasing functions is considered, and conditions for nonnegativity of the fundamental solution are found. The problem of determining if the solution stabilizes as $t\to\infty$ is solved for a model equation with constant coefficients.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 39:3, 1263–1280

Bibliographic databases:

UDC: 517.944+512.625.5
MSC: Primary 35K30; Secondary 11S80, 46F12, 35K05

Citation: A. N. Kochubei, “Parabolic equations over the field of $p$-adic numbers”, Izv. Akad. Nauk SSSR Ser. Mat., 55:6 (1991), 1312–1330; Math. USSR-Izv., 39:3 (1992), 1263–1280

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

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