A Lipschitz metric for $$\alpha $$ α -dissipative solutions to the Hunter–Saxton equation

Katrin Grunert () and Matthew Tandy ()
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Katrin Grunert: NTNU Norwegian University of Science and Technology
Matthew Tandy: NTNU Norwegian University of Science and Technology

Partial Differential Equations and Applications, 2024, vol. 5, issue 4, 1-33

Abstract: Abstract We explore the Lipschitz stability of solutions to the Hunter–Saxton equation with respect to the initial data. In particular, we study the stability of $$ \alpha $$ α -dissipative solutions constructed using a generalised method of characteristics approach, where $$\alpha $$ α is a function determining the energy loss at each position in space.

Keywords: Hunter–Saxton equation; Lipschitz stability; $$\alpha $$ α -Dissipative solutions; Primary 35B35; 37L15; Secondary 35Q35; 35L67 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s42985-024-00293-z

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