Existence and Continuous Dependence of the Local Solution of a Non-Homogeneous Equation of Order Multiple of Four
DOI:
https://doi.org/10.14738/aivp.1305.19327Keywords:
Uniqueness solution, fourth order equation, non-homogeneous equation, periodic Sobolev spaces, Fourier Theory, calculus in Banach spacesAbstract
In this article, we prove that initial value problem associated to the non- homogeneous n-th order equation in periodic Sobolev spaces with n multiple of four has a local solution 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 - Semigroup inspired by the work of Iorio [1] and Santiago [5].
References
Iorio, R. and Iorio, V. Fourier Analysis and partial Differential Equations. Cambridge University, 2002.
Liu, Z. and Zheng, S. Semigroups associated with dissipative system. Chapman Hall/CRC, 1999.
Pathack, H. K. An introduction to Nonlinear analysis and fixed point theory. Springer, Singapur, 2018.
Santiago Ayala, Y. and Rojas, S. Regularity and wellposedness of a problem to one parameter and its behavior at the limit, Bulletin of the Allahabad Mathematical Society, 32(02)(2017), 207-230.
Santiago Ayala, Y. and Rojas, S. Existencia y regularidad de solución de la ecuación del calor en espacios de Sobolev periódico, Selecciones Matemáticas, 06(01)(2019), 49-65.
Santiago Ayala, Y. Wellposedness of a Cauchy problem associated to even order equation, European Journal of Applied Sciences, 12(06)(2024), 512-530.
Santiago Ayala, Y. Existence and continuous dependence of the local solution of non homogeneous third order equation and generalizations, Transactions on Machine Learning and Artificial Intelligence, 10(5)(2022), 43-56.
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Copyright (c) 2025 Yolanda Silvia Santiago Ayala, David Sáenz López
This work is licensed under a Creative Commons Attribution 4.0 International License.
