Logarithmic convexity of non-symmetric time-fractional diffusion equations

S. E. Chorfi; L. Maniar; M. Yamamoto

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arXiv · 2404.14046

Logarithmic convexity of non-symmetric time-fractional diffusion equations

S. E. Chorfi·L. Maniar·M. Yamamoto

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Abstract

We consider a class of diffusion equations with the Caputo time-fractional derivative $\partial_t^\alpha u=L u$ subject to the homogeneous Dirichlet boundary conditions. Here, we consider a fractional order $0<\alpha < 1$ and a second-order operator $L$ which is elliptic and non-symmetric. In this paper, we show that the logarithmic convexity extends to this non-symmetric case provided that the drift coefficient is given by a gradient vector field. Next, we perform some numerical experiments to validate the theoretical results in both symmetric and non-symmetric cases. Finally, some conclusions and open problems will be mentioned.

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BibTeX RIS

S. E. Chorfi, L. Maniar, M. Yamamoto. 2024-04-22. Logarithmic convexity of non-symmetric time-fractional diffusion equations. https://arxiv.org/abs/2404.14046

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