Nonhomogeneous Wave Equation
Jan 1, 2021
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1 min read
Summary
This lecture is on Duhamel’s principle to solve the nonhomogenous initial-value problem:
$$ \left\{ \begin{alignedat}{2} u_{tt} -\Delta u &= f\quad &&\text{in}~\mathbb{R}^n \times(0,\infty)\\\ u=g\quad u_t&=h&&\text{on}~\mathbb{R}^n \times \\{t=0\\} \end{alignedat} \right. $$where $n\geq 2$ and $f\in C^{[n/2]+1}(\mathbb{R}^n \times [0,\infty))$.
