scholarly journals Singular Cauchy problem for the general Euler-Poisson-Darboux equation

2018 ◽  
Vol 16 (1) ◽  
pp. 23-31 ◽  
Author(s):  
E.L. Shishkina
Keyword(s):  
Cauchy Problem ◽  
Bessel Operator ◽  
Singular Cauchy Problem ◽  
Darboux Equation

AbstractIn this paper we obtain the solution of the singular Cauchy problem for the Euler-Poisson-Darboux equation when differential Bessel operator acts by each variable.

scholarly journals Solution of the singular Cauchy problem for a general inhomogeneous Euler–Poisson–Darboux equation

2018 ◽  
Vol 34 (2) ◽  
pp. 255-267
Author(s):  
ELINA SHISHKINA ◽  
Keyword(s):  
Cauchy Problem ◽  
Initial Conditions ◽  
Bessel Operator ◽  
Second Derivative ◽  
Singular Cauchy Problem ◽  
Classical Formulation ◽  
The Cauchy Problem ◽  
Darboux Equation

In this paper, we solve Cauchy problem for a general form of an inhomogeneous Euler–Poisson–Darboux equation, where Bessel operator acts instead of the each second derivative. In the classical formulation, the Cauchy problem for this equation is not correct. However, for a specially selected form of the initial conditions, the equation has a solution. The general form of the Euler–Poisson–Darboux equation with such conditions we will call the singular Cauchy problem.

Weak solution of the singular Cauchy problem of Euler-Poisson-Darboux equation for n=4

2013 ◽  
Vol 7 ◽  
pp. 315-325
Author(s):  
A. Manyonge ◽  
D. Kweyu ◽  
J. Bitok ◽  
H. Nyambane ◽  
J. Maremwa
Keyword(s):  
Cauchy Problem ◽  
Weak Solution ◽  
Singular Cauchy Problem ◽  
Darboux Equation
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