Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie
General information
Latest issue
Submit a manuscript

Search papers
Search references

Latest issue
Current issues
Archive issues
What is RSS

Vestnik YuUrGU. Ser. Mat. Model. Progr.:

Personal entry:
Save password
Forgotten password?

Vestnik YuUrGU. Ser. Mat. Model. Progr., 2017, Volume 10, Issue 2, Pages 107–123 (Mi vyuru376)  

This article is cited in 6 scientific papers (total in 6 papers)

Programming & Computer Software

Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity

M. O. Korpusov, D. V. Lukyanenko, E. A. Ovsyannikov, A. A. Panin

Lomonosov Moscow State University, Moscow, Russian Federation

Abstract: An initial-boundary value problem for plasma ion-sound wave equation is considered. Boltzmann distribution is approximated by a quadratic function. The local (in time) solvability is proved and the analitycal-numerical investigation of the solution's decay is performed for the considered problem. The sufficient conditions for solution's decay and an upper bound of the decay moment are obtained by the test function method. In some numerical examples, the estimation is specified by Richardson's mesh refinement method. The time interval for numerical modelling is chosen according to the decay moment's analytical upper bound. In return, numerical calculations refine the moment and the space-time pattern of the decay. Thus, analytical and numerical parts of the investigation amplify each other.

Keywords: blow-up; nonlinear initial-boundary value problem; Sobolev type equation; exponential nonlinearity; Richardson extrapolation.


Full text: PDF file (686 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.957+519.6
MSC: 35Q60, 35G31, 65L04, 65L12
Received: 07.03.2017

Citation: M. O. Korpusov, D. V. Lukyanenko, E. A. Ovsyannikov, A. A. Panin, “Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017), 107–123

Citation in format AMSBIB
\by M.~O.~Korpusov, D.~V.~Lukyanenko, E.~A.~Ovsyannikov, A.~A.~Panin
\paper Local solvability and decay of the solution of an equation with quadratic noncoercive nonlineatity
\jour Vestnik YuUrGU. Ser. Mat. Model. Progr.
\yr 2017
\vol 10
\issue 2
\pages 107--123

Linking options:

    SHARE: FaceBook Twitter Livejournal

    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. M. O. Korpusov, D. V. Lukyanenko, A. D. Nekrasov, “Analytic-numerical investigation of combustion in a nonlinear medium”, Comput. Math. Math. Phys., 58:9 (2018), 1499–1509  mathnet  crossref  crossref  isi  elib
    2. I. I. Kolotov, A. A. Panin, “On Nonextendable Solutions and Blow-Ups of Solutions of Pseudoparabolic Equations with Coercive and Constant-Sign Nonlinearities: Analytical and Numerical Study”, Math. Notes, 105:5 (2019), 694–706  mathnet  crossref  crossref  mathscinet  isi  elib
    3. M. O. Korpusov, A. K. Matveeva, D. V. Lukyanenko, “Diagnostika mgnovennogo razrusheniya resheniya v nelineinom uravnenii teorii voln v poluprovodnikakh”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 12:4 (2019), 104–113  mathnet  crossref
    4. M. O. Korpusov, E. A. Ovsyannikov, “Blow-up instability in non-linear wave models with distributed parameters”, Izv. Math., 84:3 (2020), 449–501  mathnet  crossref  crossref  isi  elib
    5. M. O. Korpusov, “Blow-up and global solubility in the classical sense of the Cauchy problem for a formally hyperbolic equation with a non-coercive source”, Izv. Math., 84:5 (2020), 930–959  mathnet  crossref  crossref  mathscinet  isi  elib
    6. M. O. Korpusov, A. A. Panin, A. E. Shishkov, “On the critical exponent “instantaneous blow-up” versus “local solubility” in the Cauchy problem for a model equation of Sobolev type”, Izv. Math., 85:1 (2021), 111–144  mathnet  crossref  crossref  mathscinet  isi
  • Number of views:
    This page:181
    Full text:50

    Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2021