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Results tagged with ap.analysis-of-pdes
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user 78164
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
83
views
Davey-Stewartson Lagrangian formulation
The system is
$i u_t + c_0 u_{xx} + u_{yy} = c_1 |u|^2 u + c_2 u \phi_x,\,$
$\phi_{xx} + c_3 \phi_{yy} = ( |u|^2 )_x.\,$
This is like the NLS but with the extra y-dimension. The NLS has the lagrang …
- 395
4
votes
1
answer
193
views
Does $u_{t}=g(t)u_{x}^{2}$ blow-up for bounded positive g? What about $u_{t}=u_{xx}+g(t)u_{x...
My original problem is to see if the following pde develops blow-ups in $(-L,L)$
$$u_{t}=u_{xx}+g(t)(u_{x})^{2}$$
for periodic boundary $u_{0}(-L)=u_{0}(L)$, where $0<g(t)<1$; specifically $g(t)=\Ph …
- 395