| Contents |
| We develop the renormalization approach for describing the asymptotic form of blowup solutions in systems of conservation laws. This approach is aimed to reveal the universal structure of renormalized solutions in a neighborhood of the blowup point. Here, the time evolution is substituted by the equivalent evolution with increasing scaling parameter, similarly to the renormalization-group (RG) method. A stationary state of the RG equations describes self-similar blowup solutions. We argue that this stationary state is an attractor of the RG equations in the space of analytic functions. The asymptotic stability of this stationary state is what implies universality of the blowup for generic initial conditions. We prove the asymptotic stability for a linearized system and make steps toward the proof of the non-linear stability. |
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