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On the null controllability of the one-dimensional heat equation with BV coefficients. (English) Zbl 1119.93311
Summary: We analyze the null controllability of the one-dimensional linear heat equation $$\rho(x)y_t-(a(x)y_x)x=0$$ with non-smooth time-independent coefficients $$\rho$$ and $$a$$. More precisely, we prove that this equation with BV coefficients is null-controllable at any positive time in the context of boundary control. The argument used in the proof relies on the exact controllability of the one-dimensional wave equation with BV coefficients and Russell’s general method (which provides the null controllability of a parabolic equation at any positive time as a consequence of the exact controllability, for large time, of the corresponding wave equation).

MSC:
 93B05 Controllability 93B07 Observability 35R05 PDEs with low regular coefficients and/or low regular data 93C20 Control/observation systems governed by partial differential equations 93C05 Linear systems in control theory