Abstract

This work is devoted to study the existence and uniqueness of solution of an analogue of the Gellerstedt problem with nonlocal assumptions on the boundary and integral gluing conditions for the parabolic-hyperbolic type equation with nonlinear terms and Gerasimov–Caputo operator of differentiation. Using the method of integral energy, the uniqueness of solution have been proved. Existence of solution was proved by the method of successive approximations of factorial law for Volterra type nonlinear integral equations.

中文翻译：

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带非线性项的带载分数式抛物双曲方程边值问题的唯一可解性

摘要

这项工作致力于研究具有非线性项和 Gerasimov-Caputo 微分算子的抛物双曲型方程的边界和积分粘合条件的非局部假设的 Gellerstedt 问题类比解的存在性和唯一性。利用积分能量法，证明了解的唯一性。利用Volterra型非线性积分方程的阶乘法逐次逼近法证明解的存在性。