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Results tagged with hyperbolic-pde
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user 102092
Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.
4
votes
1
answer
421
views
Intuition behind using energy estimate to prove existence and uniqueness of solution for Hyp...
I am trying to understand the intution behind use of energy estimate to prove existence and uniqueness(which is clear the energy estimate) of solution to hyperbolic equations. What is the basic idea b …
3
votes
1
answer
2k
views
Examples of Log-Lipschitz and nonLog-Lipschitz functions satisfying certain conditions
A function $f$ is Log-Lipschitz if there exists a constant $C >0$ such that
\begin{equation}
|f(x) - f(y)| \le C|x-y| |\log|x-y||
\end{equation}
I am trying to construct two functions with the follow …
3
votes
0
answers
60
views
Cone condition for Wave equation with Singular Speed
Consider a wave equation of the form
$$
\partial_t^2u(t,x)-c(t)^2\partial_x^2u(t,x)=0, \quad (t,x)\in (0,1]\times \mathbb{R}
$$
where the speed $c(t)$ is in $L^1([0,1]) \cap C^1((0,1])$. This woul …
0
votes
1
answer
49
views
References for the study of parameter dependent symbols $s(t,x,\xi)$ having low regularity i...
I am currently studying parameter dependent symbols, $s(t,x,\xi)$, where $t\in [0,1],x\in \Omega, \xi \in \mathbb{R^n}$. I wanted to know how the low regularity (for example, $s$ is just continuous w. …