Blow-up rate of sign-changing solutions to nonlinear parabolic systems
Erbol Zhanpeisov
TL;DR
This paper estimates the blow-up rate of sign-changing solutions to nonlinear parabolic systems, specifically the Gross-Pitaevskii system, extending previous scalar results to systems with Sobolev subcritical nonlinearity.
Contribution
It extends existing blow-up rate estimates from scalar equations to parabolic systems like the Gross-Pitaevskii system with Sobolev subcritical nonlinearity.
Findings
Provides a blow-up rate estimate for solutions to the system.
Extends scalar blow-up results to systems.
Applicable to Sobolev subcritical nonlinearities.
Abstract
We present a blow-up rate estimate for a solution to the parabolic Gross-Pitaevskii and related systems on entire space with Sobolev subcritical nonlinearity. We extend the results of [Y. Giga, S. Matsui and S. Sasayama, Indiana Univ. Math. J. {53} (2004), 483--514] to the parabolic systems.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering