scholarly journals Local existence and uniqueness of solutions of the Stefan Problem with surface tension and kinetic undercooling

1992 ◽  
Vol 164 (2) ◽  
pp. 350-362 ◽  
Author(s):  
Xinfu Chen ◽  
Fernando Reitich
Keyword(s):  
Surface Tension ◽  
Stefan Problem ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Uniqueness Of Solutions ◽  
Local Existence And Uniqueness ◽  
Kinetic Undercooling

Local existence and uniqueness of a stefan problem with surface tension

1996 ◽  
Vol 60 (3-4) ◽  
pp. 219-240 ◽  
Author(s):  
F. Abergell ◽  
D. Hilhorstl ◽  
F. Issard-Rochl ◽  
J.F. Scheid
Keyword(s):  
Surface Tension ◽  
Stefan Problem ◽  
Existence And Uniqueness ◽  
Local Existence ◽  
Local Existence And Uniqueness

LOCAL EXISTENCE AND UNIQUENESS THEORY FOR THE SECOND SOUND EQUATION IN ONE SPACE DIMENSION

2012 ◽  
Vol 09 (01) ◽  
pp. 177-193 ◽  
Author(s):  
KEIICHI KATO ◽  
YUUSUKE SUGIYAMA
Keyword(s):  
Cauchy Problem ◽  
Existence And Uniqueness ◽  
Space Dimension ◽  
Local Existence ◽  
Second Sound ◽  
Uniqueness Of Solutions ◽  
Local Existence And Uniqueness ◽  
The Cauchy Problem ◽  
Time Existence ◽  
Uniqueness Theory

We study the local-in-time existence and uniqueness of the Cauchy problem for the nonlinear wave equation [Formula: see text], which is called the second sound equation. Assuming that u(0, x) = φ ≥ A > 0, φ ∈ C1, and ∂xφ ∈ Hs, we establish the uniqueness of solutions without restriction on their amplitude.

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