Blow-up results for vector-valued nonlinear heat equations with no gradient structure. (English) Zbl 0902.35050

The author constructs a blow-up solution for the following nonlinear complex equation \[ u_{t}=\Delta u+(1+i\delta)| u| ^{p-1}u,\qquad u\in {\mathbb{C}}. \] The asymptotic profile near the singularity is obtained, as well as a generalization of the results to other vector-valued equations is proposed.


35K40 Second-order parabolic systems
35B40 Asymptotic behavior of solutions to PDEs
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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