The classical heat equation compared with a hyperbolic one: A pointwise estimate for the difference between their solutions. (English) Zbl 0597.35083
The authors study the asymptotic behaviour of the solution u of the Cauchy problem for the equation \(\epsilon u_{tt}+u_ t=\lambda u_{xx}.\) They prove the estimate \(| u-u^ 0| \leq C\epsilon\), where \(u^ 0\) solves the Cauchy problem for the above equation with \(\epsilon =0\) and C depends on the initial data.
Reviewer: M.Kopáčková
MSC:
| 35L80 | Degenerate hyperbolic equations |
| 35L05 | Wave equation |
| 35M99 | Partial differential equations of mixed type and mixed-type systems of partial differential equations |
| 35B45 | A priori estimates in context of PDEs |
| 35K05 | Heat equation |
