Abstract:
In this paper we introduce a new partial differential equation, which is an extension of the known Euler — Darboux equation. On the base of the proven properties of solution to introduced equation we explicitly find general solutions for various values of parameters, prove existence and uniqueness theorems. Basing on the general solutions of introduced equation, we solve the Cauchy problems and modified Cauchy problems in an upper right triangle. We find explicit solutions and prove the existence and uniqueness theorems for the posed problems.
Keywords:Euler — Darboux problem, Cauchy problem, general solution, solvability.
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