Existence and Continuous Dependence of the Local Solution of Non Homogeneous Third Order Equation and Generalizations
Keywords:Uniqueness solution, third order equation, non homogeneous equation, n-th order equation, periodic Sobolev spaces, Fourier Theory, cal- culus in Banach spaces.
In this article, we prove that initial value problem associated to the non homogeneous third order equation in periodic Sobolev spaces has a local so- lution in [0, T ] with T > 0, and the solution has continuous dependence with respect to the initial data and the non homogeneous part of the problem. We do this in a intuitive way using Fourier theory and introducing a Co - Semi- group inspired by the work of Iorio  and Santiago . Also, we prove the uniqueness solution of the homogeneous third order equa- tion, using its conservative property, inspired by the work of Iorio  and Santiago . Finally, we study its generalization to n-th order equation.
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Copyright (c) 2022 Yolanda Santiago Ayala
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