TY - JOUR
T1 - Abstract time-dependent transport equations
AU - Beals, R.
AU - Protopopescu, V.
PY - 1987/2/1
Y1 - 1987/2/1
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.
UR - https://www.scopus.com/pages/publications/0023293235
U2 - 10.1016/0022-247X(87)90252-6
DO - 10.1016/0022-247X(87)90252-6
M3 - Article
AN - SCOPUS:0023293235
SN - 0022-247X
VL - 121
SP - 370
EP - 405
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -