Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential


Biccari U. Boundary controllability for a one-dimensional heat equation with a singular inverse-square potential, Mathematical Control and related fields, DOI:

Abstract: We analyse controllability properties for the one-dimensional heat equation with singular inverse-square potential u_t-u_{xx}-\frac{\mu}{x^2}u=0\,\,\,(x,t)\in(0,1)\times(0,T). For any \mu <1/4, we prove that the equation is null controllable through a boundary control f\in H^1(0,T) acting at the singularity point x=0. This result is obtained employing the moment method by Fattorini and Russell.

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