View source for Samokhin A. Gradient catastrophes for Burgers equation on a finite interval. Numerical and qualitative study, talk Workshop Geom. of PDEs and Integrability, 14-18 Oct 2013, Teplice nad Becvou, Czech Rep. (abstract)

{{MeetingTalk
| speaker = Alexey Samokhin
| title = Gradient catastrophes for Burgers equation on a finite interval. Numerical and qualitative study
| abstract = We consider initial value-boundary problem (IVBP) for the Burgers equation 

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<math>u_t(x,t)=u_{xx}(x,t)+2\eta u(x,t)u_x(x,t)</math>

on a finite interval:

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<math>u(x,0) =f(x), \quad u(\alpha,t) = l(t), \quad u(\beta,t) =r(t), \quad x\in[\alpha,\beta]</math>.

The case of constant boundary conditions <math>u(\alpha,t) = A, \quad u(\beta,t) =B</math> and its asymptotics is of special interest here. For such a IVBP viscosity usually produces asymptotic stationary solution which is invariant for some subalgebra of the full symmetry algebra of the equation. But the evolution may also result in a stable gradient catastrophe.
| slides = 
| references = 
| 79YY-MM-DD = 7986-89-85
}}