Uniform convergence of multigroup approximation of the transport equation. (Chinese) Zbl 0922.47062
To solve a transport equation, we usually use the multigroup solution to approximate the original solution. [A. Belleni-Morante, “Multigroup Neutron Transport”, J. Math. Phys. (1972)]. However, the convergence is not uniformly in general.
This paper considers the transport operator \(A\) in Banach space \(L^\infty(G)\). We have a local Lipschitz continuously integral semigroup \(S(T)\). Under a slight limitation, aid by the \(S(t)\) generated from \(A\), the authors show some results on the existence and uniqueness of nonnegative solution for a transport equation. Meanwhile, the approximation is also uniformly.
This paper considers the transport operator \(A\) in Banach space \(L^\infty(G)\). We have a local Lipschitz continuously integral semigroup \(S(T)\). Under a slight limitation, aid by the \(S(t)\) generated from \(A\), the authors show some results on the existence and uniqueness of nonnegative solution for a transport equation. Meanwhile, the approximation is also uniformly.
Reviewer: Zhang Dian-zhou (Shanghai)
MSC:
| 47N20 | Applications of operator theory to differential and integral equations |
| 82C70 | Transport processes in time-dependent statistical mechanics |
