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Title: Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities

Abstract

The Cauchy problem with non-negative continuous initial function for the equation u{sub t}={delta}u{sup m}-u{sup p}, (x,t) element of S=R{sup N} x R{sub +}, is considered for 0<p<1, p<m. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as t{yields}{infinity} are established.

Authors:
 [1]
  1. Pedagogical Institute, Vitebsk (Belarus)
Publication Date:
OSTI Identifier:
21202918
Resource Type:
Journal Article
Journal Name:
Sbornik. Mathematics
Additional Journal Information:
Journal Volume: 191; Journal Issue: 3; Other Information: DOI: 10.1070/SM2000v191n03ABEH000462; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1064-5616
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAUCHY PROBLEM; EQUATIONS; FUNCTIONS; MATHEMATICAL SOLUTIONS

Citation Formats

Gladkov, A L. Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities. United States: N. p., 2000. Web. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Gladkov, A L. Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities. United States. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
Gladkov, A L. Sun . "Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities". United States. doi:10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA).
@article{osti_21202918,
title = {Behaviour of solutions of certain quasilinear parabolic equations with power-type non-linearities},
author = {Gladkov, A L},
abstractNote = {The Cauchy problem with non-negative continuous initial function for the equation u{sub t}={delta}u{sup m}-u{sup p}, (x,t) element of S=R{sup N} x R{sub +}, is considered for 0<p<1, p<m. For generalized solutions of this problem with initial data increasing at infinity several results on their behaviour as t{yields}{infinity} are established.},
doi = {10.1070/SM2000V191N03ABEH000462; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)},
journal = {Sbornik. Mathematics},
issn = {1064-5616},
number = 3,
volume = 191,
place = {United States},
year = {2000},
month = {4}
}