A VARIATIONAL APPROACH TO SELF-SIMILAR SOLUTIONS FOR SEMILINEAR HEAT EQUATIONS

EQUADIFF 2003 ◽  
2005 ◽  
Author(s):  
YŪKI NAITO
Keyword(s):  
Variational Approach ◽  
Heat Equations ◽  
Self Similar ◽  
Similar Solutions

scholarly journals Full self-similar solutions of the subsonic radiative heat equations

2015 ◽  
Vol 22 (8) ◽  
pp. 082109 ◽  
Author(s):  
Tomer Shussman ◽  
Shay I. Heizler
Keyword(s):  
Radiative Heat ◽  
Heat Equations ◽  
Self Similar ◽  
Similar Solutions

On Uniqueness and Stability of Self-Similar Blow-Up Solutions of Nonlinear Heat Equations: Evolution Approach

2003 ◽  
Vol 05 (03) ◽  
pp. 329-348 ◽  
Author(s):  
Manuela Chaves ◽  
Victor A. Galaktionov
Keyword(s):  
Parabolic Equations ◽  
Blow Up ◽  
Domain Of Attraction ◽  
Nonlinear Parabolic Equations ◽  
Heat Equations ◽  
Nonlinear Parabolic ◽  
Linear Parabolic Equations ◽  
Self Similar ◽  
Similar Solutions ◽  
Evolution Approach

We present evolution arguments of studying uniqueness and asymptotic stability of blow-up self-similar solutions of second-order nonlinear parabolic equations from combustion and filtration theory. The analysis uses intersection comparison techniques based on the Sturm Theorem on zero set for linear parabolic equations. We show that both uniqueness and stability of similarity ODE profiles are directly related to the asymptotic structure of their domain of attraction relative to the corresponding parabolic evolution.

ON APPROXIMATE SELF-SIMILAR SOLUTIONS OF A CLASS OF QUASILINEAR HEAT EQUATIONS WITH A SOURCE

1985 ◽  
Vol 52 (1) ◽  
pp. 155-180 ◽  
Author(s):  
V A Galaktionov ◽  
S P Kurdyumov ◽  
A A Samarskiĭ
Keyword(s):  
Heat Equations ◽  
Self Similar ◽  
Similar Solutions

Asymptotically self-similar behaviour of global solutions for semilinear heat equations with algebraically decaying initial data

2019 ◽  
Vol 150 (2) ◽  
pp. 789-811
Author(s):  
Yūki Naito
Keyword(s):  
Initial Data ◽  
Existence Of Solutions ◽  
Global Solutions ◽  
Heat Equations ◽  
Complicated Manner ◽  
The Cauchy Problem ◽  
Self Similar ◽  
The One ◽  
Image Position ◽  
Similar Solutions

AbstractWe consider the Cauchy problem $$\left\{ {\matrix{ {u_t = \Delta u + u^p,\quad } \hfill & {x\in {\bf R}^N,\;t \leq 0,} \hfill \cr {u(x,0) = u_0(x),\quad } \hfill & {x\in {\bf R}^N,} \hfill \cr } } \right.$$where N > 2, p > 1, and u0 is a bounded continuous non-negative function in RN. We study the case where u0(x) decays at the rate |x|−2/(p−1) as |x| → ∞, and investigate the convergence property of the global solutions to the forward self-similar solutions. We first give the precise description of the relationship between the spatial decay of initial data and the large time behaviour of solutions, and then we show the existence of solutions with a time decay rate slower than the one of self-similar solutions. We also show the existence of solutions that behave in a complicated manner.

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