Estimates for solutions to the transport equation under the perturbation of its attenuation and scattering terms

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Daiki Tanaka
Nobuyuki Higashimori
Yuusuke Iso


The aim of the paper is to give $L^p$-estimates for the weak solution to the transport equation with $L^\infty$-perturbation both of the attenuation coefficient and of the scattering kernel. We try to clarify the constants in our estimates, and we show the estimates by a direct calculation. We introduce the albedo operator for the solutions, and we show stability of perturbed albedo operators.

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Tanaka, D., Higashimori, N., & Iso, Y. (2012). Estimates for solutions to the transport equation under the perturbation of its attenuation and scattering terms. Tamkang Journal of Mathematics, 43(2), 313–320.


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