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Results tagged with ap.analysis-of-pdes
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user 146723
Partial differential equations (PDEs): Existence and uniqueness, regularity, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDEs, conservation laws, qualitative dynamics.
1
vote
1
answer
158
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Existence theorem of weak solutions of $u_t+f(u)u_x=0$
Consider this PDE:
$\begin{cases}u_t+f(u)u_x=0\\ u(x,0)=\varphi(x)\end{cases}$
Has this PDE weak solutions whatever is $f$ or $\varphi$? I want to find an existence theorem and bibliography about that …
- 6,367
0
votes
0
answers
217
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Solving PDE $u_t+f(u)u_x=0$ using its physical interpretation
Let's be this PDE:
$\begin{cases}u_t+f(u)u_x=0\\
u(x,0)=\varphi(x) \end{cases}$
and $f\in 1-1$.
I have these thoughts:
We can imagine $x'x$ having sticky particles. As we know $\frac{dx}{dt}=f(u)$. …
- 189
1
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0
answers
116
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Burgers PDE with piecewise constant initial condition
Let's deal with this Burgers PDE:
You can see the characteristic curves below:
I believe the breaking time is $\boldsymbol{t_b=0}$, because it is the $\inf$ of $t$-coordinates of the intersection p …
- 189