Local Similarity Solutions for the Initial-value Problem in Non-linear Diffusion

1983 ◽  
Vol 30 (2) ◽  
pp. 209-214 ◽  
Author(s):  
R. E. GRUNDY
Keyword(s):  
Initial Value Problem ◽  
Similarity Solutions ◽  
Local Similarity ◽  
Initial Value ◽  
Linear Diffusion ◽  
Non Linear

scholarly journals Asymmetric bifurcation

1980 ◽  
Vol 21 (3) ◽  
pp. 297-304 ◽  
Author(s):  
S. Rosenblat
Keyword(s):  
Diffusion Equation ◽  
Initial Value Problem ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Initial Value ◽  
Linear Diffusion ◽  
Non Linear ◽  
Bifurcation And Stability

AbstractA study is made of a non-linear diffusion equation which admits bifurcating solutions in the case where the bifurcation is asymmetric. An analysis of the initial-value problem is made using the method of multiple scales, and the bifurcation and stability characteristics are determined. It is shown that a suitable interpretation of the results can lead to determination of the choice of the bifurcating solution adopted by the system.

ON THE CAUCHY PROBLEM IN BESOV SPACES FOR A NON-LINEAR SCHRÖDINGER EQUATION

2000 ◽  
Vol 02 (02) ◽  
pp. 243-254 ◽  
Author(s):  
FABRICE PLANCHON
Keyword(s):  
Cauchy Problem ◽  
Schrödinger Equation ◽  
Initial Value Problem ◽  
Schrodinger Equation ◽  
Initial Value ◽  
Non Linear ◽  
The Cauchy Problem ◽  
Self Similar ◽  
Similar Solutions ◽  
Well Posed

We prove that the initial value problem for a non-linear Schrödinger equation is well-posed in the Besov space [Formula: see text], where the nonlinearity is of type |u|αu. This allows to obtain self-similar solutions, and to recover previous results under weaker smallness assumptions on the data.

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