TY - JOUR

T1 - GLOBAL WELL-POSEDNESS AND EXPONENTIAL STABILITY FOR THE FERMION EQUATION IN WEIGHTED SOBOLEV SPACES

AU - Sun, Baoyan

AU - Wu, Kung Chien

N1 - Funding Information:
2020 Mathematics Subject Classification. Primary: 82C40, 47H20, 35B40. Key words and phrases. Fermion equation, polynomial weight, spectral gap, dissipativity, semigroup, exponential rate. The first author is supported by the Scientific Research Foundation of Yantai University grant 2219008. The second author is supported by the Ministry of Science and Technology under the grant 110-2636-M-006-005-and National Center for Theoretical Sciences. ∗ Corresponding author: Baoyan Sun.
Funding Information:
The first author is supported by the Scientific Research Foundation of Yantai University grant 2219008. The second author is supported by the Ministry of Science and Technology under the grant 110-2636-M-006-005- and National Center for Theoretical Sciences.
Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

PY - 2022/5

Y1 - 2022/5

N2 - This work deals with the Cauchy problem and the asymptotic behavior of the solution of the fermion equation in the Sobolev spaces with a polynomial weight in the torus. We first investigate the linearized equation and obtain the optimal exponential decay rate for the associated semigroup. Our strategy is taking advantage of quantitative spectral gap estimates in smaller reference Hilbert space, the factorization method and the enlargement of the functional space. We then turn to the nonlinear equation and prove the global existence and uniqueness of solutions in a close-to-equilibrium regime. Moreover, we prove an exponential stability for such a solution with the optimal decay rate given by the semigroup decay of the linearized equation.

AB - This work deals with the Cauchy problem and the asymptotic behavior of the solution of the fermion equation in the Sobolev spaces with a polynomial weight in the torus. We first investigate the linearized equation and obtain the optimal exponential decay rate for the associated semigroup. Our strategy is taking advantage of quantitative spectral gap estimates in smaller reference Hilbert space, the factorization method and the enlargement of the functional space. We then turn to the nonlinear equation and prove the global existence and uniqueness of solutions in a close-to-equilibrium regime. Moreover, we prove an exponential stability for such a solution with the optimal decay rate given by the semigroup decay of the linearized equation.

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U2 - 10.3934/dcdsb.2021147

DO - 10.3934/dcdsb.2021147

M3 - Article

AN - SCOPUS:85128278228

VL - 27

SP - 2537

EP - 2562

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

IS - 5

ER -