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Long time existence of a class of perturbations of planar shock fronts for second order hyperbolic conservation laws. (English) Zbl 0719.35056
By reducing the shock front problem of the form $(1)\quad \sum_{0\leq i\leq N}\partial_ i(H^ i(\phi '))=0,\text{ where } \phi '=(\partial_ 0\phi,\partial_ x\phi),\quad \partial_ i=\partial /\partial x_ i,\quad \partial_ x\phi =(\partial_ 1\phi,...,\partial_ N\phi),$ to a mixed problem in a quarter space via the partial hodograf transform a global planar shock front solution satisfying Lax type entropy conditions is studied.
It is shown that small $$C^{\infty}$$ compatible perturbations with compact support of the data give rise to shock fronts with long lifespan (if $$N\geq 5)$$ which remain stable and almost planar.
Reviewer: K.Zlateva (Russe)

##### MSC:
 35L65 Hyperbolic conservation laws 35B20 Perturbations in context of PDEs 35L67 Shocks and singularities for hyperbolic equations 35L70 Second-order nonlinear hyperbolic equations
##### Keywords:
Lax type entropy conditions; long lifespan
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##### References:
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