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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Convection-induced singularity suppression in the Keller-Segel and other non-linear PDEs
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by Gautam Iyer, Xiaoqian Xu and Andrej Zlatoš PDF
Trans. Amer. Math. Soc. 374 (2021), 6039-6058 Request permission


In this paper we study the effect of the addition of a convective term, and of the resulting increased dissipation rate, on the growth of solutions to a general class of non-linear parabolic PDEs. In particular, we show that blow-up in these models can always be prevented if the added drift has a small enough dissipation time. We also prove a general result relating the dissipation time and the effective diffusivity of stationary cellular flows, which allows us to obtain examples of simple incompressible flows with arbitrarily small dissipation times.

As an application, we show that blow-up in the Keller-Segel model of chemotaxis can always be prevented if the velocity field of the ambient fluid has a sufficiently small dissipation time. We also study reaction-diffusion equations with ignition-type nonlinearities, and show that the reaction can always be quenched by the addition of a convective term with a small enough dissipation time, provided the average initial temperature is initially below the ignition threshold.

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Additional Information
  • Gautam Iyer
  • Affiliation: Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
  • MR Author ID: 753706
  • ORCID: 0000-0001-9638-0455
  • Email:
  • Xiaoqian Xu
  • Affiliation: Zu Chongzhi Center of Mathematical and Computational Science, Duke Kunshan University, People’s Republic of China
  • Email:
  • Andrej Zlatoš
  • Affiliation: Department of Mathematics, UC San Diego, La Jolla, California 92130
  • Email:
  • Received by editor(s): August 5, 2019
  • Received by editor(s) in revised form: March 27, 2020
  • Published electronically: June 7, 2021
  • Additional Notes: This work has been partially supported by the National Science Foundation under grants DMS-1652284 and DMS-1900943 to AZ, and DMS-1814147 to GI, as well as by the Center for Nonlinear Analysis.
  • © Copyright 2021 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 6039-6058
  • MSC (2020): Primary 35B44; Secondary 35B27, 35Q35, 76R05
  • DOI:
  • MathSciNet review: 4302154