Electron. J. Differential Equations, Vol. 2020 (2020), No. 129, pp. 1-25.

Pointwise estimates of solutions to conservation laws with nonlocal dissipation-type terms

Fengbai Li, Weike Wang, Yutong Wang

Abstract:
This article concerns the Cauchy problem of conservation laws with nonlocal dissipation-type terms in R3. By using Green's function and the time-frequency decomposition method, we study global classical solutions and their long time behavior including pointwise estimates for large initial data, for solutions near the nontrivial equilibrium state.

Submitted February 12, 2020. Published December 22, 2020.
Math Subject Classifications: 35A01, 35A22, 35A25.
Key Words: Conservation law; dissipation; Cauchy problem; equilibrium state; Green's function; time-frequency decomposition method; pointwise estimate.
DOI: 10.58997/ejde.2020.129

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Fengbai Li
School of Mathematics
Shanghai University of Finance and Economics
777 Guo Ding Road, Shanghai 200433, China
email: li.fengbai@mail.shufe.edu.cn
Weike Wang
School of Mathematical Sciences and Institute of Natural Sciences
Shanghai Jiao Tong University
800 Dong Chuan Road
Shanghai 200240, China
email: wkwang@sjtu.edu.cn
Yutong Wang
School of Mathematical Sciences
Shanghai Jiao Tong University
800 Dong Chuan Road
Shanghai 200240, China
email: wyt0521@sjtu.edu.cn

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