Abstract time-dependent transport equations

R. Beals; V. Protopopescu

doi:10.1016/0022-247X(87)90252-6

Abstract time-dependent transport equations

R. Beals
, V. Protopopescu

Research output: Contribution to journal › Article › peer-review

121 Scopus citations

Abstract

We consider the abstract time-dependent linear transport equation as an initial-boundary value evolution problem in the Banach spaces L_p, 1 ≤ p < ∞, or on a space of measures on a (possibly time-dependent) kinetic phase space. Existence, uniqueness, dissipativity, and positivity results are proved for very general, possibly time-dependent, transport operators and boundary conditions. When the phase space, boundary conditions, and transport operator are independent of time, corresponding results are obtained for the associated semigroup.

Original language	English
Pages (from-to)	370-405
Number of pages	36
Journal	Journal of Mathematical Analysis and Applications
Volume	121
Issue number	2
DOIs	https://doi.org/10.1016/0022-247X(87)90252-6
State	Published - Feb 1 1987

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title = "Abstract time-dependent transport equations",

abstract = "We consider the abstract time-dependent linear transport equation as an initial-boundary value evolution problem in the Banach spaces Lp, 1 ≤ p < ∞, or on a space of measures on a (possibly time-dependent) kinetic phase space. Existence, uniqueness, dissipativity, and positivity results are proved for very general, possibly time-dependent, transport operators and boundary conditions. When the phase space, boundary conditions, and transport operator are independent of time, corresponding results are obtained for the associated semigroup.",

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N2 - We consider the abstract time-dependent linear transport equation as an initial-boundary value evolution problem in the Banach spaces Lp, 1 ≤ p < ∞, or on a space of measures on a (possibly time-dependent) kinetic phase space. Existence, uniqueness, dissipativity, and positivity results are proved for very general, possibly time-dependent, transport operators and boundary conditions. When the phase space, boundary conditions, and transport operator are independent of time, corresponding results are obtained for the associated semigroup.

AB - We consider the abstract time-dependent linear transport equation as an initial-boundary value evolution problem in the Banach spaces Lp, 1 ≤ p < ∞, or on a space of measures on a (possibly time-dependent) kinetic phase space. Existence, uniqueness, dissipativity, and positivity results are proved for very general, possibly time-dependent, transport operators and boundary conditions. When the phase space, boundary conditions, and transport operator are independent of time, corresponding results are obtained for the associated semigroup.

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ER -

Abstract time-dependent transport equations

Abstract

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