## Abstract

We consider the following parabolic system whose nonlinearity has no gradient structure: {∂_{t}u=Δu+e^{pv},∂_{t}v=μΔv+e^{qu},u(⋅,0)=u_{0},v(⋅,0)=v_{0},p,q,μ>0, in the whole space R^{N}. We show the existence of a stable blowup solution and obtain a complete description of its singularity formation. The construction relies on the reduction of the problem to a finite dimensional one and a topological argument based on the index theory to conclude. In particular, our analysis uses neither the maximum principle nor the classical methods based on energy-type estimates which are not supported in this system. The stability is a consequence of the existence proof through a geometrical interpretation of the quantities of blowup parameters whose dimension is equal to the dimension of the finite dimensional problem.

Original language | English (US) |
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Pages (from-to) | 7523-7579 |

Number of pages | 57 |

Journal | Journal of Differential Equations |

Volume | 264 |

Issue number | 12 |

DOIs | |

State | Published - Jun 15 2018 |

## Keywords

- Blowup profile
- Blowup solution
- Semilinear parabolic system
- Stability

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics