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On the Faedo–Galerkin Method for Non-autonomous Nonlinear Differential Systems

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Abstract

This article contemplates a non-autonomous nonlinear differential system in a separable Hilbert space \(\mathcal {X}\). The projection operators are used to confine our concern to a finite-dimensional subspace of \(\mathcal {X}\). The existence, uniqueness, and convergence of approximate solutions are explored by making use of the hypothesis of fractional powers of a closed linear operator. We also analyze the Faedo–Galerkin approximation of the solution. An example is also built to exhibit the significance of the acquired results.

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Acknowledgements

The work of the first author is supported by IoE, University of Delhi.

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  1. Surendra Kumar and Paras Sharma have contributed equally to this work.

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  1. Department of Mathematics, University of Delhi, New Delhi, Delhi, 110007, India

    Surendra Kumar & Paras Sharma

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  1. Surendra Kumar
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  2. Paras Sharma
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Correspondence to Surendra Kumar.

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Kumar, S., Sharma, P. On the Faedo–Galerkin Method for Non-autonomous Nonlinear Differential Systems. Results Math 78, 107 (2023). https://doi.org/10.1007/s00025-023-01894-7

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