Global solvability of the Cauchy problem for the Yang-Mills-HIGGS equations

1987 ◽  
Vol 37 (1) ◽  
pp. 802-822 ◽  
Author(s):  
M. V. Goganov ◽  
L. V. Kapitanskii
Keyword(s):  
Cauchy Problem ◽  
Global Solvability ◽  
Yang Mills ◽  
The Cauchy Problem

Global existence and non-existence for the degenerate and uniformly parabolic equations with gradient term

2013 ◽  
Vol 143 (3) ◽  
pp. 643-668 ◽  
Author(s):  
Haifeng Shang
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Parabolic Equations ◽  
Existence Of Solutions ◽  
Local Existence ◽  
Global Solvability ◽  
Gradient Term ◽  
Global Existence Of Solutions ◽  
The Cauchy Problem ◽  
Limiting Case

We study the Cauchy problem for the degenerate and uniformly parabolic equations with gradient term. The local existence, global existence and non-existence of solutions are obtained. In the case of global solvability, we get the exact estimates of a solution. In particular, we obtain the global existence of solutions in the limiting case.

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