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): Difference between revisions
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| speaker = Alexey Samokhin | | speaker = Alexey Samokhin | ||
| title = Gradient catastrophes for Burgers equation on a finite interval. Numerical and qualitative study | | 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 | | abstract = We consider initial value-boundary problem (IVBP) for the Burgers equation | ||
<math>u_t(x,t)=u_{xx}(x,t)+2\eta u(x,t)u_x(x,t)</math> | <math>u_t(x,t)=u_{xx}(x,t)+2\eta u(x,t)u_x(x,t)</math> | ||
on a finite interval: | |||
<math>u(x,0) =f(x), \quad u(\alpha,t) = l(t), \quad u(\beta,t) =r(t), \quad x\in[\alpha,\beta]</math>. | <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, | The case of constant boundary conditions <math>u(\alpha,t) = A</math>, <math>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 = | | slides = [[Media:Samokhin A. Gradient catastrophes for a generalized Burgers equation on a finite interval (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).zip|Samokhin A. Gradient catastrophes for a generalized Burgers equation on a finite interval (presentation at The Workshop on Geometry of PDEs and Integrability, 14-18 October 2013, Teplice nad Becvou, Czech Republic).zip]] | ||
| references = | | references = | ||
| 79YY-MM-DD = 7986-89-85 | | 79YY-MM-DD = 7986-89-85 | ||
}} | }} | ||
Latest revision as of 13:12, 13 November 2013
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
on a finite interval:
.
![{\displaystyle u(x,0)=f(x),\quad u(\alpha ,t)=l(t),\quad u(\beta ,t)=r(t),\quad x\in [\alpha ,\beta ]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e1ca2c3251538df416d131f45b120fc48442dd75)
The case of constant boundary conditions , 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.
