A Cauchy-Goursat Problem for the generalized Eulera-Poisson-Darboux equation

2016 ◽  
Vol 4 (1) ◽  
Author(s):  
Akhmadjon K Urinov ◽  
Akhrorjon I Ismoilov ◽  
Azizbek O Mamanazarov
Keyword(s):  
Goursat Problem ◽  
Darboux Equation

Strong scheme for a stochastic Goursat problem

2004 ◽  
Vol 150 (2) ◽  
pp. 351-363
Author(s):  
Shu-Shiang Huang ◽  
Yenkun Huang ◽  
Che-Yuan Tsai
Keyword(s):  
Goursat Problem

On the Euler-Poisson-Darboux equation

1970 ◽  
Vol 23 (1) ◽  
pp. 89-102 ◽  
Author(s):  
A. Erdélyi
Keyword(s):  
Darboux Equation

scholarly journals Zero Sets of Solutions of the Generalized Darboux Equation

2017 ◽  
Vol 2 (4) ◽  
pp. 272-280
Author(s):  
Valery Volchkov ◽  
◽  
Vitaly Volchkov ◽  
Keyword(s):  
Zero Sets ◽  
Darboux Equation

scholarly journals Wiener-Hopf equation and Fredholm property of the Goursat problem in Gevrey space

1994 ◽  
Vol 135 ◽  
pp. 165-196 ◽  
Author(s):  
Masatake Miyake ◽  
Masafumi Yoshino
Keyword(s):  
Differential Equations ◽  
Differential Operators ◽  
Newton Polygon ◽  
Index Theorem ◽  
Fredholm Property ◽  
Goursat Problem ◽  
Point Of View ◽  
Partial Differential ◽  
Partial Differential Operators ◽  
Gevrey Spaces

In the study of ordinary differential equations, Malgrange ([Ma]) and Ramis ([R1], [R2]) established index theorem in (formal) Gevrey spaces, and the notion of irregularity was nicely defined for the study of irregular points. In their studies, a Newton polygon has a great advantage to describe and understand the results in visual form. From this point of view, Miyake ([M2], [M3], [MH]) studied linear partial differential operators on (formal) Gevrey spaces and proved analogous results, and showed the validity of Newton polygon in the study of partial differential equations (see also [Yn]).

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