The article introduces a numerical algorithm for α-dissipative solutions of the Hunter-Saxton equation. It discusses key properties and challenges related to wave breaking phenomena. The method involves a tailored projection operator to handle approximation errors effectively. The study highlights the significance of correct design choices in maintaining convergence and accuracy throughout the solution process. Various mathematical structures and extensions related to the Hunter-Saxton equation are explored, providing insights into weak solutions, energy dissipation, and concentration measures. The research contributes to advancing numerical schemes for conservative and dissipative solutions, offering a comprehensive approach to handling singularities and energy distribution in complex mathematical models.
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arxiv.org
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