Green functions for the initial-value problem
Tags: #physics #green functionsEquation
$$u(x,t)=\int\limits_{-\infty}^\infty f(x')Q(x,x',t)dx'+ \int\limits_{-\infty}^\infty g(x')P(x,x',t)dx'$$Latex Code
u(x,t)=\int\limits_{-\infty}^\infty f(x')Q(x,x',t)dx'+ \int\limits_{-\infty}^\infty g(x')P(x,x',t)dx'
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Introduction
Equation
Latex Code
u(x,t)=\int\limits_{-\infty}^\infty f(x')Q(x,x',t)dx'+ \int\limits_{-\infty}^\infty g(x')P(x,x',t)dx' \\
\begin{aligned} Q(x,x',t)&=&\frac{1}{2} [\delta(x-x'-vt)+\delta(x-x'+vt)]\\ P(x,x',t)&=& \left\{\begin{array}{ll} \displaystyle \frac{1}{2v}&~~~\mbox{if}~~|x-x'|vt \end{array}\right.\end{aligned} \\
\displaystyle Q(x,x',t)=\frac{\partial P(x,x',t)}{\partial t}
Explanation
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