本文選題：腔體 + 散射�。� 參考：《中山大學(xué)學(xué)報(bào)(自然科學(xué)版)》2017年02期

【摘要】：利用變分法研究了全涂層的可穿透腔體散射問(wèn)題的解的存在唯一性。首先,應(yīng)用Green公式把微分方程轉(zhuǎn)化為積分方程后,由Rellich引理和唯一延拓原理,證明了全涂層的可穿透腔體散射問(wèn)題的解的唯一性。然后,由Dirichlet-to-Neumann算子理論、跡定理、連續(xù)嵌入定理和Lax-Milgram引理,證明了全涂層的可穿透腔體散射問(wèn)題的解的存在性。
[Abstract]:The existence and uniqueness of the solution to the scattering problem of a fully coated penetrating cavity are studied by using the variational method. Firstly, after the differential equation is transformed into an integral equation by Green's formula, the uniqueness of the solution of the scattering problem of a fully coated penetrating cavity is proved by the Rellich Lemma and the unique continuation principle. Then, by using Dirichlet-to-Neumann operator theory, trace theorem, continuous embedding theorem and Lax-Milgram Lemma, we prove the existence of solutions to the scattering problem of a fully coated penetrating cavity.
【作者單位】： 重慶師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院;
【基金】：國(guó)家自然科學(xué)基金數(shù)學(xué)天元青年基金(11426052) 重慶市教育委員會(huì)科學(xué)技術(shù)研究項(xiàng)目(KJ1400522,KJ1600329) 2013年重慶高校創(chuàng)新團(tuán)隊(duì)建設(shè)計(jì)劃項(xiàng)目(KJTD201308)
【分類(lèi)號(hào)】：O175

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