Abstract Conventional plane harmonic waves decay in direction of propagation, but unconventional harmonic waves grow in the direction of propagation. While a single unconventional wave cannot be a solution to a physically meaningful boundary value problem, these waves may have an essential contribution to the overall solution of a problem as long as this is a superposition of unconventional and conventional waves. A fourth order diffusion equation with proper thermodynamic structure, and the Burnett equations of rarefied gas dynamics exhibit conventional and unconventional waves. Steady state oscillating boundary value problems are considered to discuss the interplay of conventional and unconventional waves. Results show that as long as the second law of thermodynamics is valid, unconventional waves may contribute to the overall solution, which, however is dominated by conventional waves, and behaves as these.

中文翻译：

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具有负空间阻尼的波是否不稳定？

摘要 常规平面谐波沿传播方向衰减，非常规谐波沿传播方向增长。虽然单个非常规波不能解决具有物理意义的边界值问题，但只要这是非常规波和常规波的叠加，这些波可能对问题的整体解决方案具有重要的贡献。具有适当热力学结构的四阶扩散方程和稀薄气体动力学的伯内特方程表现出常规和非常规波。考虑稳态振荡边值问题来讨论常规波和非常规波的相互作用。结果表明，只要热力学第二定律成立，非常规波就可能有助于整体解，即：