On the continuous dependence on the coefficients of evolutionary equations

Marcus Waurick

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arXiv · 1606.07731

On the continuous dependence on the coefficients of evolutionary equations

Marcus Waurick

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Abstract

In an abstract Hilbert space setting, we discuss many linear phenomena of mathematical physics. The functional analytic framework presented is used to address continuous dependence of the solution operators $\mathcal{S}(\mathcal{M})$ of certain (linear partial differential) equations on the coefficients $\mathcal{M}$. For this, we introduce a particular class of coefficients $\mathcal{M}$ and study the (nonlinear) mapping $\mathcal{M}\mapsto \mathcal{S}(\mathcal{M})$. We provide criteria that guarantee the continuity of $\mathcal{S}(\cdot)$ under the norm, the strong, and the weak operator topology. We exemplify our findings in non-autonomous electro-magnetic theory, thermodynamics and acoustics.

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Marcus Waurick. 2016-06-24. On the continuous dependence on the coefficients of evolutionary equations. https://arxiv.org/abs/1606.07731

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