Preventing blow up by convective terms in dissipative PDEs

Clicks: 39
ID: 283414
2015
Free PDF
Article Quality & Performance Metrics
Overall Quality
Not rated
Combines reader engagement with the AI quality analysis. This article has not been analysed, so there is no overall score — reader engagement is measured and shown alongside.
AI Quality Assessment
Not analyzed
Readership in this journal
Popular

Ranked #704 of 803 articles by views in arXiv

Most read Least read

Bar heights use a square-root scale. Only the 120 most-read articles are drawn; the journal has 803 in total.

Mint this article as an NFT
Not yet minted

Create a permanent, verifiable on-chain record of this article on the Scimatic Network. The NFT is held in your Journament account, and you can withdraw it to your own wallet at any time.

5 SUSD one-off · no wallet required
Sign in to mint
Abstract
We study the impact of the convective terms on the global solvability or finite time blow up of solutions of dissipative PDEs. We consider the model examples of 1D Burger's type equations, convective Cahn-Hilliard equation, generalized Kuramoto-Sivashinsky equation and KdV type equations, we establish the following common scenario: adding sufficiently strong (in comparison with the destabilizing nonlinearity) convective terms to equation prevents the solutions from blowing up in finite time and makes the considered system globally well-posed and dissipative and for weak enough convective terms the finite time blow up may occur similarly to the case when the equation does not involve convective term. This kind of result has been previously known for the case of Burger's type equations and has been strongly based on maximum principle. In contrast to this, our results are based on the weighted energy estimates which do not require the maximum principle for the considered problem.
Reference Key
zelik2015preventing Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Bilgesu Bilgen; Varga Kalantarov; Sergey Zelik
Journal arXiv
Year 2015
DOI
DOI not found
URL
http://arxiv.org/abs/1509.03845v1
Keywords
math.ap 35a01, 35b44, 35b45

Citations

No citations found. To add a citation, contact the admin at info@scimatic.org

Comments

No comments yet. Be the first to comment on this article.