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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.

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Unique continuation for the wave equation

Try $u(x,t) = x_1 t$ with $\Gamma = \{x:\; x_1 = 0\}$.
Robert Israel's user avatar
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First order pde with characteristics

This pde can be solved formally as $$ u(x,y) = F(y - B(x)) $$ where $B(x)$ is an antiderivative of $1/b(x)$ and $F$ is an arbitrary differentiable function. Of course at points where $b(x)$ is disco …
Robert Israel's user avatar
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Analytic solution of a system of linear, hyperbolic, first order, partial differential equat...

For simplicity, consider solutions where $ u$ does not depend on $x, y$: $A u_t + B(t) u = 0$. If $y^T A = 0$, that says $y^T B(t) u = 0$, so $u$ is restricted to belong to a certain (possibly $t$-d …
Robert Israel's user avatar