Linear partial differential equations in module of formal generalized functions over commutative ring

DOI10.1007/S10958-021-05505-0zbMath1482.35076OpenAlexW3198541789WikidataQ115382137 ScholiaQ115382137MaRDI QIDQ1983988

Sergey L. Gefter, A. L. Piven'

Publication date: 13 September 2021

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-021-05505-0

zbMATH Keywords

Cauchy problemformal generalized functions

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Initial value problems for second-order hyperbolic equations (35L15) Initial value problems for linear higher-order PDEs (35G10) PDEs of infinite order (35R50) Transport equations (35Q49)

Related Items (1)

Infinite-order differential operators in the module of formal generalized functions and in a ring of formal power series

Cites Work

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• Fundamental solution of an implicit linear inhomogeneous first order differential equation over an arbitrary ring
• Cauchy problem for evolution equations with an infinite-order differential operator. II.
• Implicit linear differential-difference equations in the module of formal generalized functions over a commutative ring
• Formal functional calculus for weakly locally nilpotent operators in Fréchet spaces
• Differential operators of infinite order in the space of formal Laurent series and in the ring of power series with integer coefficients
• Fundamental solution of the simplest implicit linear differential equation in a vector space

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