English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The paper considers a linear system of Boltzmann transport equationsmodelling the evolution of three species of particles, photons, electrons andpositrons. The system is coupled because of the collision term (an integraloperator). The model is intended especially for dose calculation (forwardproblem) in radiation therapy. It, however, does not apply to all relevantinteractions in its present form. We show under physically relevant assumptionsthat the system has a unique solution in appropriate ($L^1$-based) spaces andthat the solution is non-negative when the data (internal source and inflowboundary source) is non-negative. In order to be self-contained as much as ispractically possible, many (basic) results and proofs have been reproduced inthe paper. Existence, uniqueness and non-negativity of solutions for therelated time-dependent coupled system are also proven. Moreover, we deal withinverse radiation treatment planning problem (inverse problem) as an optimalcontrol problem both for external and internal therapy (in general$L^p$-spaces). Especially, in the case $p=2$ variational equations for anoptimal control related to an appropriate differentiable convex object functionare verified. Its solution can be used as an initial point for an actual(global) optimization.

On Existence of $L^1$-solutions for Coupled Boltzmann Transport Equation and Radiation Therapy Treatment Optimization