WELL POSEDNESS FOR THE GOOD BOUSSINESQ EQUATION WITH INTERNAL DISSIPATION
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Abstract
This article focuses on the study of the good Boussinesq equation, proving the existence and uniqueness of solutions in periodic Sobolev spaces for s ≥ 2. The adopted strategy consists of first analyzing a particular case, in which one of the equation’s coefficients is identically zero, and then extending the results to the general case through an iterative procedure based on the fixed-point method. To achieve this, fundamental tools such as Semigroup Theory and Fourier Analysis are employed.
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