Partial differential equations First-order equations and conservation laws Concept
Cole–Hopf transformation
Summary
The Cole–Hopf transformation turns the viscous Burgers' equation into the linear heat equation. It sets , where is a positive solution of the heat equation. It gives an explicit formula for the solution of the initial value problem for Burgers' equation. Letting the viscosity tend to zero in that formula recovers the entropy solution of the inviscid equation. See the definition.
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| Tag | VBMQ9SJ3DH |
|---|---|
| URI | m2://VBMQ9SJ3DH |
| Kind | concept |
| Writing | W0 stub |
| MSC | 35Q35, 35K05, 35A22 |
| Same as |
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