Publication: IDENTIFICACIÓN DE UN COEFICIENTE DESCONOCIDO EN LA ECUACIÓN DE KURAMOTO-SIVASHINSKY
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Date
2019
Authors
GAJARDO MIRANDA, DIEGO FERNANDO
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Abstract
En este trabajo, estudiamos el problema inverso de recuperar el coefi ciente de antidifusión = (x) en la ecuación de Kuramoto-Sivashinsky lineal ut + (o(x)uxx)xx +(x)uxx = 0 a partir de una medición en tiempo nal m(x) = u(x; T), x 2 (0; 1).Usando un enfoque de control optimal formulamos el problema inverso como un problema de minimización. De este problema mostramos la existencia de un mínimo yderivamos las condiciones de optimalidad. Luego, usando estimaciones de energía del sistema y las condiciones de optimalidad, deducimos la estabilidad y unicidad siempre que T sea su cientemente pequeño. Finalmente, presentamos simulaciones numéricaspara la reconstrucción del parámetro y.
In this work, we study the inverse problem of retrieving the unknown coefficient = (x) in the Kuramoto-Sivashinsky equation ut + (o(x)uxx)xx + (x)uxx = 0 fromthe nal time measurement m(x) = u(x; T), x 2 (0; 1).By using an optimal control approach we formulate the inverse problem as a minimizationproblem. For this problem we show the existence of a minimum and we derivethe optimality conditions. Then, by using energy estimates and the optimality conditions,we deduce the stability and uniqueness provided T is sufficiently small. Finally,we present some numerical experiments for the reconstruction of the parameter .
In this work, we study the inverse problem of retrieving the unknown coefficient = (x) in the Kuramoto-Sivashinsky equation ut + (o(x)uxx)xx + (x)uxx = 0 fromthe nal time measurement m(x) = u(x; T), x 2 (0; 1).By using an optimal control approach we formulate the inverse problem as a minimizationproblem. For this problem we show the existence of a minimum and we derivethe optimality conditions. Then, by using energy estimates and the optimality conditions,we deduce the stability and uniqueness provided T is sufficiently small. Finally,we present some numerical experiments for the reconstruction of the parameter .
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Catalogado desde la version PDF de la tesis.
Keywords
COEFICIENTE DE ANTIDIFUSION , ECUACION DE KURAMOTO-SIVASHINSKY , PROBLEMA INVERSO