Existencia y unicidad de soluciones d´ebiles para la ecuaci´on de onda con coeficientes variables
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Date
2024
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Universidad Nacional de Trujillo
Abstract
En este trabajo se ha establecido condiciones necesarias y suficientes para que la ecuación de onda con coeficientes variables tenga solución débil única. Se prueba que si los coeficientes son esencialmente acotados, usando la norma del supremo, entonces existe solución débil y es única. Se usa el método de Galerkin para proyectar a espacios finito dimensionales obteniendo aproximaciones para luego obtener convergencias débiles en espacios de Sobolev
Abstract In this work, necessary and sufficient conditions have been established for the wave equation with variable coefficients to have a unique weak solution. It is proved that if the coefficients are essentially bounded, using the supremum norm, then a weak solution exists and is unique. The Galerkin method is used to project to finite-dimensional spaces obtaining approximations and then obtaining weak convergences in Sobolev spaces
Abstract In this work, necessary and sufficient conditions have been established for the wave equation with variable coefficients to have a unique weak solution. It is proved that if the coefficients are essentially bounded, using the supremum norm, then a weak solution exists and is unique. The Galerkin method is used to project to finite-dimensional spaces obtaining approximations and then obtaining weak convergences in Sobolev spaces
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Keywords
Ecuación de onda, Método de Galerkin, Espacios de Sobolev