On fundamental solution of Helmholtz equation
数学专题报告
报告题目(Title)：On fundamental solution of Helmholtz equation
报告人(Speaker)：Huyan Chen (SIMIS, Shanghai)
地点(Place)：后主楼1124
时间(Time)：2025年10月22日（周三）14:30-15:30
邀请人(Inviter)：熊金钢
报告摘要
This talk investigates the fundamental solutions of general-order Helmholtz operators in whole space. We propose two distinct approaches to approximate the complex-valued fundamental solution: one relying on the Fourier transform in the complex domain, and another establishing a connection with the classical case for comparison and validation. We rigorously analyze the asymptotic behavior at infinity of the real and imaginary parts, and examine the validity of the Sommerfeld radiation condition, which ensures uniqueness of the outgoing solution in scattering problems. Furthermore, we derive Sobolev-type embedding inequalities via convolution with the real part of the fundamental solution and extend these estimates to broader function spaces using classical interpolation theorems.
