scholarly journals Degenerate parabolic differential equations: Necessity of the well- posedness of the Cauchy problem

1974 ◽  
Vol 14 (3) ◽  
pp. 461-476
Author(s):  
Masatake Miyake
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Well Posedness ◽  
Parabolic Differential Equations ◽  
The Cauchy Problem ◽  
Degenerate Parabolic

ON THE CAUCHY PROBLEM FOR SOME PSEUDO-DIFFERENTIAL EQUATIONS OF SCHRÖDINGER TYPE

1996 ◽  
Vol 06 (03) ◽  
pp. 295-314 ◽  
Author(s):  
R. AGLIARDI ◽  
D. MARI
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fundamental Solution ◽  
Differential Equations ◽  
Lower Order ◽  
Order Term ◽  
Well Posedness ◽  
Gevrey Spaces ◽  
The Cauchy Problem ◽  
Pseudo Differential Equation

A fundamental solution of the Cauchy problem is constructed for a pseudo-differential equation generalizing some Schrödinger equations. Then well-posedness of the Cauchy problem is proved in some Gevrey spaces whose indices depend on the lower order term of the operator.

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