Large time behavior of solutions for a Cauchy problem on a nonlinear conservation law with large initial data in the whole space. (English) Zbl 1390.35444
Summary: We consider the Cauchy problem on a nonlinear conversation law with large initial data. By Green’s function methods, energy methods, Fourier analysis, and frequency decomposition, we obtain the global existence and the optimal time-decay estimate of solutions.
MSC:
| 35S05 | Pseudodifferential operators as generalizations of partial differential operators |
| 35S10 | Initial value problems for PDEs with pseudodifferential operators |
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