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Results tagged with hyperbolic-pde
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user 42326
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
Let $\Omega$ be a bounded region in $\mathbb{R}^n$ and $\Gamma \subset \subset \partial \Omega$, assume $u$ solves the wave equation
$$u_{tt}-c(x)\Delta u=0, \ \ u(x,0)=f(x),$$
where $f$ and $1-c$ …
1
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1
answer
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Global solutions of the wave equation with bounded initial condition
Let $f,g$ be bounded compactly supported smooth functions, and assume $u$ is the solutions of the wave equation
$$u_{tt}-c^2(x)\Delta u=0 \ \ \hbox{on} \ \ \mathbb{R}^n \times (0,\infty)$$
$$u(x,0)=f, …
5
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3
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453
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Structure of sign changes under the heat flow
Let $f$ be a smooth function on $R^2$, and define $N_f$ to be the set of points $p$ such that the nodal set of $f$ ($\{x\in R^2: f(x)=0\}$) divided every neighborhood of $p$ into four regions. Indeed, …