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  1. Nonlinear Differential Equations and Applications NoDEA
  2. Nonlinear Differential Equations and Applications NoDEA : Volume 12
  3. Nonlinear Differential Equations and Applications NoDEA : Volume 12, Issue 2, August 2005
  4. Asymptotical self-similarity in nonlinear parabolic systems
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Nonlinear Differential Equations and Applications NoDEA : Volume 23
Nonlinear Differential Equations and Applications NoDEA : Volume 22
Nonlinear Differential Equations and Applications NoDEA : Volume 21
Nonlinear Differential Equations and Applications NoDEA : Volume 20
Nonlinear Differential Equations and Applications NoDEA : Volume 19
Nonlinear Differential Equations and Applications NoDEA : Volume 18
Nonlinear Differential Equations and Applications NoDEA : Volume 17
Nonlinear Differential Equations and Applications NoDEA : Volume 16
Nonlinear Differential Equations and Applications NoDEA : Volume 15
Nonlinear Differential Equations and Applications NoDEA : Volume 14
Nonlinear Differential Equations and Applications NoDEA : Volume 13
Nonlinear Differential Equations and Applications NoDEA : Volume 12
Nonlinear Differential Equations and Applications NoDEA : Volume 12, Issue 4, January 2006
Nonlinear Differential Equations and Applications NoDEA : Volume 12, Issue 3, December 2005
Nonlinear Differential Equations and Applications NoDEA : Volume 12, Issue 2, August 2005
On the existence and uniqueness of minimizers for a class of integral functionals
Asymptotical self-similarity in nonlinear parabolic systems
Fourth order equations of critical Sobolev growth. Energy function and solutions of bounded energy in the conformally flat case
A blow up result for a fractionally damped wave equation
A nondegeneracy result for a nonlinear elliptic equation
An improved Hardy-Sobolev inequality in W1,p and its application to Schrödinger operators
Nonlinear Differential Equations and Applications NoDEA : Volume 12, Issue 1, May 2005
Nonlinear Differential Equations and Applications NoDEA : Volume 11
Nonlinear Differential Equations and Applications NoDEA : Volume 10
Nonlinear Differential Equations and Applications NoDEA : Volume 9
Nonlinear Differential Equations and Applications NoDEA : Volume 8
Nonlinear Differential Equations and Applications NoDEA : Volume 7
Nonlinear Differential Equations and Applications NoDEA : Volume 6
Nonlinear Differential Equations and Applications NoDEA : Volume 5
Nonlinear Differential Equations and Applications NoDEA : Volume 4

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Asymptotical self-similarity in nonlinear parabolic systems

Content Provider SpringerLink
Author Rencłlawowicz, Joanna
Copyright Year 2005
Abstract We prove that blowing up solutions of the system $$u_{{it}} - d_{i} \Delta u_{i} = {\prod\limits_{k = 1}^m {u_{k} ^{{p_{k} ^{i} }} ,} }\quad i = 1, \ldots ,m,\;x \in \mathbb{R}^{N} ,\;t > 0,$$ $$u_{i} (0,x) = u_{{0i}} (x),\quad i = 1, \ldots ,m,\;x \in \mathbb{R}^{N} ,$$ where m > 1 and pki ≤ 0, behave like self-similar solutions to this system near the blow up point. In the case m = 2 we obtain more precise result.
Ending Page 169
Page Count 19
Starting Page 151
File Format PDF
ISSN 10219722
e-ISSN 14209004
Journal Nonlinear Differential Equations and Applications NoDEA
Issue Number 2
Volume Number 12
Language English
Publisher Birkhäuser-Verlag
Publisher Date 2005-01-01
Publisher Place Basel
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword reaction–diffusion system Liouville theorem Analysis blow up asymptotic behaviour Reaction-diffusion equations semilinear systems Asymptotic behavior of solutions Nonlinear parabolic equations
Content Type Text
Resource Type Article
Subject Applied Mathematics Analysis
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