Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator

Shi, Wenbei

doi:10.3390/math11010061

Mathematics

2022

DOI: 10.3390/math11010061

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Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator

Wenbei Shi

Abstract: In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes.

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Large-Time Behavior of Momentum Density Support of a Family of Weakly Dissipative Peakon Equations with Higher-Order Nonlinearity

Dong

2023

Mathematics

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In this paper, we mainly study the weakly dissipative peakon equations with higher-order nonlinearity. Under the effect of dissipation, we first derive the infinite propagation speed if the initial datum has a nonnegative compact support. Furthermore, we obtain the large-time behavior of the support of momentum density with the initial data compactly supported. The corresponding results are obtained by using some prior estimates and the energy method. It is worth noting that we need to overcome the difficulties caused by the high-order nonlinear structure and the dissipative effect of the equation. The obtained results generalize the previous results to a certain degree.

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Large-Time Behavior of Momentum Density Support of a Family of Weakly Dissipative Peakon Equations with Higher-Order Nonlinearity

Dong

2023

Mathematics

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Liouville-Type Theorem for Nonlinear Elliptic Equations Involving Generalized Greiner Operator

Abstract: In this paper, we study the Liouville-type behaviors of the generalized Greiner operators with nonlinear boundary value conditions. We use the technique based upon the method of moving planes.

Cited by 1 publication

References 21 publications

Large-Time Behavior of Momentum Density Support of a Family of Weakly Dissipative Peakon Equations with Higher-Order Nonlinearity

Large-Time Behavior of Momentum Density Support of a Family of Weakly Dissipative Peakon Equations with Higher-Order Nonlinearity

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