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Results tagged with ap.analysis-of-pdes
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user 9245
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
Imaginary exponential functional of Brownian motion
For those interested, we have released today an ArXiv preprint with what we were able to find: http://arxiv.org/abs/1101.1173
- 141
0
votes
Imaginary exponential functional of Brownian motion
It turns out that the above generating function pde is related to a Lax pair of Painlevé III/Sine-Gordon, at least for the parameter value g=2.
As soon as I have written this up, I'll post details
- 141
4
votes
3
answers
1k
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Imaginary exponential functional of Brownian motion
Thanks to the work by M. Yor and colleagues, much is known about the following exponential of Brownian motion:
$X= \int_0^{\infty}{\rm d}t \ e^{-t + g \ B(t)}$
where $g$ is a real scale parameter.
…
- 141
5
votes
2
answers
802
views
Blow-up for the quasilinear heat equation $u_t= u \ u_{x x}$ or the related $w_t= \left(w_x ...
What kind of approaches can be used to study the following quasilinear parabolic pde
for a scalar function $u=u(x,t)$ ?
$$
u_t= u \ u_{x x}
$$
The physical problem where this pde comes from dictates …
- 141