An Inverse Piston Problem with Small BV Initial Data
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In this paper, we consider an inverse piston problem with small BV initial data for the system of one-dimensional adiabatic flow. Suppose that the original state of the gas on the right side of the piston and the position of the forward shock are known, then we can globally solve the inverse piston problem and estimate the speed of the piston in a unique manner.
KeywordsQuasilinear hyperbolic system Bounded variation norm Inverse piston problem One-dimensional adiabatic flow
Mathematics Subject Classification (2000)35L45 35L60 35R30
The authors would like to thank Prof. Tatsien Li for his constant support and encouragement. This work is supported by the National Natural Science Foundation of China, No. 11371095 and No. 11771091.