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Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation

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Abstract

Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u{sub t} = {Delta} u{sup {sigma}+1} + u{sup {beta}} are found in the case {beta} = {sigma} + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case {beta}>{sigma} + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs.
Authors:
Vasileva, D P [1] 
  1. Bylgarska Akademiya na Naukite, Sofia (Bulgaria). Matematischeski Inst.
Publication Date:
Dec 31, 1993
Product Type:
Technical Report
Report Number:
JINR-E-11-93-369
Reference Number:
SCA: 990200; PA: AIX-25:032106; EDB-94:073070; NTS-94:020632; SN: 94001192749
Resource Relation:
Other Information: PBD: 1993
Subject:
99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; BOUNDARY-VALUE PROBLEMS; ASYMPTOTIC SOLUTIONS; NONLINEAR PROBLEMS; STABILITY; 990200; MATHEMATICS AND COMPUTERS
OSTI ID:
10144858
Research Organizations:
Joint Inst. for Nuclear Research, Dubna (Russian Federation). Lab. of Computing Techniques and Automation
Country of Origin:
JINR
Language:
English
Other Identifying Numbers:
Other: ON: DE94622700; TRN: XJ9406306032106
Availability:
OSTI; NTIS (US Sales Only); INIS
Submitting Site:
INIS
Size:
16 p.
Announcement Date:
Jul 05, 2005

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Citation Formats

Vasileva, D P. Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation. JINR: N. p., 1993. Web.
Vasileva, D P. Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation. JINR.
Vasileva, D P. 1993. "Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation." JINR.
@misc{etde_10144858,
title = {Numerical analysis of the asymptotic behavior of solutions of a boundary problem for a nonlinear parabolic equation}
 author = {Vasileva, D P}
 abstractNote = {Blow-up and global time self-similar solutions of a boundary problem for a nonlinear equation u{sub t} = {Delta} u{sup {sigma}+1} + u{sup {beta}} are found in the case {beta} = {sigma} + 1. It is shown that they describe the asymptotic behavior of a wide class of initial perturbations. A numerical investigation of the solutions in the case {beta}>{sigma} + 1 is also made. A hypothesis is done that the behavior for large times of global time solutions is described by the self-similar solutions of the equation without source.(author). 20 refs.; 9 figs.}
 place = {JINR}
 year = {1993}
 month = {Dec}
 }