The entropy weak solution to a generalized Fornberg–Whitham equation

• Main Authors: Nan Li, Shaoyong Lai
• Format: Article
• Language: English
• Published: SpringerOpen 2020-05-01
• Series: Boundary Value Problems
• Subjects: Entropy weak solutions; Existence and uniqueness; The Fornberg–Whitham equation
• Online Access: http://link.springer.com/article/10.1186/s13661-020-01400-w

Abstract We investigate a nonlinear generalized Fornberg–Whitham equation. The key element is that we derive an L 2 ( R ) $L^{2}(\mathbb{R})$ conservation law for solutions of the equation. We establish several estimates by utilizing the L 2 ( R ) $L^{2}(\mathbb{R})$ conservation law. These estimates lead to the proof of the existence and uniqueness of entropy weak solution of the equation in the space L 1 ( R ) ∩ L ∞ ( R ) $L^{1}(\mathbb{R})\cap L^{\infty}(\mathbb{R})$ .