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Classical
solutions of the Fornberg–Whitham equation
Georgia Burkhalter, Ryan C. Thompson and Madison Waldrep |
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Vol. 18 (2025), No. 2, 239–260
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Abstract |
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We prove well-posedness in (a.k.a. classical solutions) of the Fornberg–Whitham equation. To achieve this objective, we study its weak formulation under a Lagrangian framework. Applying the fundamental theorem of ordinary differential equations to the generated semilinear system, we then construct a unique solution to the equation that is continuously dependent on the initial data. These results improve upon others in Sobolev and Besov spaces. |
Keywords
Fornberg–Whitham equation, Cauchy problem, Sobolev spaces,
well-posedness, classical solutions, diffeomorphisms,
conserved quantities
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Mathematical Subject Classification
Primary: 35Q53
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Milestones
Received: 19 December 2022
Revised: 12 September 2023
Accepted: 6 November 2023
Published: 26 February 2025
Communicated by Kenneth S. Berenhaut
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Authors |
| Georgia Burkhalter | |
| Department of Mathematics University of North Georgia Dahlonega, GA United States |
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| Ryan C. Thompson | |
| Department of Mathematics University of North Georgia Dahlonega, GA United States |
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| Madison Waldrep | |
| Department of Mathematics University of North Georgia Dahlonega, GA United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
