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On the singular cauchy problem for a generalization of the Euler-Poisson-Darboux equation in two space variables (1955)

Diaz, J. B. ; Ludford, G. S. S.

Springer

Annali di matematica pura ed applicata 38 (1955), S. 33-50

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ISSN: 1618-1891

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary The present paper contains an existence and uniqueness theorem for the singularCauchy problem for the non-homogeneousEuler-Poisson-Darboux equation: $$\begin{gathered} u_{xx} + u_{yy} - u_{tt} - \frac{k}{t}u_t = f(x,y,t),t 〉 0,k 〉 0, \hfill \\ u(x,y,0) = u_t (x,y,0) = 0. \hfill \\ \end{gathered}$$ The solution of this problem is used to prove an existence and uniqueness theorem for the following singularCauchy problem: $$\begin{gathered} u_{xx} + u_{yy} - u_{tt} - \frac{k}{t}u_t - h(x,y,t)u = 0,t 〉 0,k 〉 0, \hfill \\ u(x,y,0) = g(x,y),u_t (x,y,0) = 0, \hfill \\ \end{gathered}$$ by the method of successive approximations.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02413513

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