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Abstract <p>We investigate a balance equation that describes a particle distribution whose evolution is driven by deterministic motion, jumps, and a non-conservative sink/source term. For the linear version of this equation, we prove the existence and uniqueness theorem for a solution in the space of nonnegative measures. We also show that the solution can be represented by a stochastic process defined on an extended phase space.</p>

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Linear Balance Equation with the Integral Term

  • 期刊论文

  • 发表日期：

    2026年1月1日

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  • Yu. V. Averboukh

摘要

Abstract

We investigate a balance equation that describes a particle distribution whose evolution is driven by deterministic motion, jumps, and a non-conservative sink/source term. For the linear version of this equation, we prove the existence and uniqueness theorem for a solution in the space of nonnegative measures. We also show that the solution can be represented by a stochastic process defined on an extended phase space.