Abstract
We discuss many interesting properties of the initial-boundary value problem for the heat equation $u_{t}(x,t) = u_{xx}(x,t)$ on $(x,t) \in (0,\infty) \times (0,\infty)$. In particular, we can prescribe the space, time, and space-time oscillation limits (limsup and liminf) of $u(x,t)$ by choosing suitable initial data $h(x)$ and boundary dada $g(t)$. We also consider singular initial-boundary value problem and oblique initial-boundary value problem for the heat equation.
Funding Statement
Research in this paper is supported by a fund from NSTC (National Science and Technology Council) of Taiwan with grant number 110-2115-M-007-005-MY2.
Acknowledgments
The author would like to thank the reviewers for their reading and suggestions on the paper. He would also like to thank Professor Cheng-Hsiung Hsu for taking care of the submission of this paper.
Citation
Dong-Ho Tsai. "On Various Space-time Properties of Solutions to the One-dimensional Heat Equation on Semi-infinite Rod." Taiwanese J. Math. Advance Publication 1 - 83, 2024. https://doi.org/10.11650/tjm/240903
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