Uniqueness Solution of the Heat Equation in Sobolev Periodic Spaces
Keywords:Uniqueness solution, heat equation, Non homogeneous equation, Periodic Sobolev spaces, Calculus in Banach Spaces
In this article, we prove the uniqueness solution of the homogeneous and non-homogeneous heat equation in periodic Sobolev spaces. We do it in a different way from what we did in , in this case we perform differential calculus in Hs-per and we take advantage of the immersion and properties of periodic Sobolev spaces. With this proof we gain to visualize the dissipative property of the homogeneous problem and with this we deduce the continuous dependence with respect to the initial data and the uniqueness solution for both cases: homogeneous and non-homogeneous.
Iorio R, Iorio V. Fourier Analysis and partial differential equation. Cambridge University, 2001.
Santiago Y, Rojas S, Quispe T. Espacios de Sobolev periódico y un problema de Cauchy asociado a un modelo de ondas en un fluido viscoso. Theorema, Segunda Época. 2016; 3(4):7-23.
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.
How to Cite
The authors who publish in this journal accept the following conditions:
1. The authors retain the copyright and assign to the journal the right of the first publication, with the work registered with the Creative Commons Attribution License,Atribución 4.0 Internacional (CC BY 4.0) which allows third parties to use what is published whenever they mention the authorship of the work And to the first publication in this magazine.
2. Authors may make other independent and additional contractual arrangements for non-exclusive distribution of the version of the article published in this journal (eg, include it in an institutional repository or publish it in a book) provided they clearly state that The paper was first published in this journal.
3. Authors are encouraged to publish their work on the Internet (for example, on institutional or personal pages) before and during the review and publication process, as it can lead to productive exchanges and to a greater and more rapid dissemination Of the published work.