DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR SOME HYPERBOLIC-ELLIPTIC SYSTEM

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概要

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• We study the decay property of a certain nonlinear hyperbolic-elliptic system with 2mth-order elliptic part, which is a modified version of the simplest radiating gas model. It is proved that, for m ≥ 2, the system verifies a decay property of the regularity-loss type that is characterized by the parameter m. This dissipative property is very weak in the high-frequency region and causes a difficulty in showing the global existence of solutions to the nonlinear problem. By employing the time-weighted energy method together with the optimal decay for lower-order derivatives of solutions, we overcome this difficulty and establish a global existence and asymptotic decay result. Furthermore, we show that the solution approaches the nonlinear diffusion wave described by the self-similar solution of the Burgers equation as time tends to infinity.

• Faculty of Mathematics, Kyushu Universityの論文

著者

• Kawashima Shuichi

  Faculty Of Mathematics Kyushu University

• Kubo Takekiyo

  Graduate School of Mathematics Kyushu University

関連論文

• Large time behavior of solutions to a semilinear hyperbolic system with relaxation (流体と気体の数学解析--RIMS研究集会報告集)
• DECAY PROPERTY OF REGULARITY-LOSS TYPE AND NONLINEAR EFFECTS FOR SOME HYPERBOLIC-ELLIPTIC SYSTEM

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