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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

3 votes
1 answer
2k views

Boundary conditions for Klein-Gordon equation

Let us consider the Klein-Gordon equation $$(\Box +m^2)u=0,$$ where $u$ is a scalar valued function, $m\geq 0$, $\Box=\frac{\partial^2}{\partial x_0^2}-\sum_{i=1}^d\frac{\partial^2}{\partial x_i^2}$. …
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3 votes
3 answers
2k views

Uniqueness of solution of the wave equation

Consider the wave equation $$\frac{\partial^2 u}{\partial t^2}-\sum_{i=1}^n\frac{\partial^2 u}{\partial x_i^2}=0$$ with initial conditions $$u|_{t=0}=\frac{\partial u}{\partial t}|_{t=0}=0$$ Does …
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2 votes
0 answers
163 views

Inhomogeneous wave equation - a reference

Consider the inhomogeneous wave equation $$\frac{\partial^2u}{\partial t^2}-\Delta u=\rho(x,t),$$ where $x=(x_1,\dots,x_n)$, $\Delta=\sum_{i=1}^n\frac{\partial^2}{\partial x_i^2}$ is the Laplacian, $\ …
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