Existence and continuous dependence of solution of the Boussinesq wave equation in periodic Sobolev spaces
Keywords:Family of strongly continuous operators, Boussinesq equation, Fourier Theory, Periodic Sobolev spaces
We will begin our study, focusing on the theory of periodic Sobolev spaces, for this we cite . Then, we will prove that the non-homogeneous Boussinesq equation has a local solution and that the solution also continually depends on the initial data and non-homogeneity, we do this intuitively using Fourier theory and in an elegant version introducing families of strongly continuous operators, inspired by the work of Iorio , Santiago and Rojas ,  and .
Iorio R, Iorio V. Analysis and Partial Differential Equations. Cambridge University, 2001.
Santiago Y, Rojas S. Existencia y dependencia continua de la solución de la ecuación de onda no homogénea en espacios de Sobolev Periódico. 2020; 07(01):52-73.
Santiago Y, Rojas S. Existencia y regularidad de solución de la ecuación del calor en espacios de Sobolev Periódico. Selecciones Matemáticas. 2019; 06(01):49-65.
Santiago Y, Rojas S. Regularity and wellposedness of a problem to one parameter and its behavior at the limit. Bulletin of the Allahabad Mathematical Society. 2017; 32(02):207-230.
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