Gellerstedt Type Problem with Integral Gluing Condition for a Mixed Type Equation with Non-linear Loaded Term

In this work, the existence and the uniqueness of solution of an analogue of the Gellerstedt type problem with integral gluing condition for a loaded mixed parabolic-hyperbolic type equation have been investigated. Considering mixed type equation has a nonlinear loaded parts. Using the method of integral energy the uniqueness of solution has been proved. The existence of solution is proved, using the well-known successive approximations method.

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