Nonhomogeneous Wave Equation
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 $f\in C^{[n/2]+1}(\mathbb{R}^n \times [0,\infty))$.