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In this paper, we discuss the \(q^2\) -analogue of the inverse source heat equation in one dimension. Namely, we consider an inverse source q-heat equation by using q-Rubin’s difference operator. Well-posedness results are presented in appropriate Sobolev-type spaces. In particular, we show that the following inverse source q-heat equation generated by q-Rubin’s difference operator has a unique solution. We also show that these solutions can be represented by explicit formulas. The presentation is based on a joint work with M. Ruzhansky and S. Shaimardan.

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On the  \(q^2\) -Analogue of the Inverse Source Heat Equation

  • 会议论文

  • 发表日期：

    2025年

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  • Irfan Ali

摘要

In this paper, we discuss the \(q^2\) -analogue of the inverse source heat equation in one dimension. Namely, we consider an inverse source q-heat equation by using q-Rubin’s difference operator. Well-posedness results are presented in appropriate Sobolev-type spaces. In particular, we show that the following inverse source q-heat equation generated by q-Rubin’s difference operator has a unique solution. We also show that these solutions can be represented by explicit formulas. The presentation is based on a joint work with M. Ruzhansky and S. Shaimardan.