On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation

By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solu...

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Bibliographic Details
Main Authors: Zongqi Liang, Huashui Zhan
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2009/827087
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spelling doaj-68c7a42c05834a5385b3f11204d8448f2020-11-24T22:44:21ZengHindawi LimitedDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/827087827087On the Cauchy Problem of a Quasilinear Degenerate Parabolic EquationZongqi Liang0Huashui Zhan1School of Science, Jimei University, Xiamen 361021, ChinaSchool of Science, Jimei University, Xiamen 361021, ChinaBy Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.http://dx.doi.org/10.1155/2009/827087
collection DOAJ
language English
format Article
sources DOAJ
author Zongqi Liang
Huashui Zhan
spellingShingle Zongqi Liang
Huashui Zhan
On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
Discrete Dynamics in Nature and Society
author_facet Zongqi Liang
Huashui Zhan
author_sort Zongqi Liang
title On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
title_short On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
title_full On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
title_fullStr On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
title_full_unstemmed On the Cauchy Problem of a Quasilinear Degenerate Parabolic Equation
title_sort on the cauchy problem of a quasilinear degenerate parabolic equation
publisher Hindawi Limited
series Discrete Dynamics in Nature and Society
issn 1026-0226
1607-887X
publishDate 2009-01-01
description By Oleinik's line method, we study the existence and the uniqueness of the classical solution of the Cauchy problem for the following equation in [0,T]×R2: ∂xxu+u∂yu−∂tu=f(⋅,u), provided that T is suitable small. Results of numerical experiments are reported to demonstrate that the strong solutions of the above equation may blow up in finite time.
url http://dx.doi.org/10.1155/2009/827087
work_keys_str_mv AT zongqiliang onthecauchyproblemofaquasilineardegenerateparabolicequation
AT huashuizhan onthecauchyproblemofaquasilineardegenerateparabolicequation
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