Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation
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DOI：
10.1142/s0219891622500126
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发表时间：
2021-06
影响因子：
0.7
通讯作者：
Takahisa Inui;Shuji Machihara
中科院分区：
文献类型：
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作者：
Takahisa Inui;Shuji Machihara
本文考虑一类具有幂型非线性项的阻尼波动方程（NLDW）到相应的热传导方程（NLH）的奇异极限问题。我们称我们的奇异极限问题为非时滞极限。我们证明了在两个正则解下，NLDW的解在[Formula：see text]拓扑中趋于NLH的解。我们还得到了正收敛速度在较弱的拓扑[公式：见正文]。此外，在幂的范围限制下，如果非线性混合问题的解是全局的且衰减到零，则得到了非时滞极限的时间上全局一致收敛性。
We consider a singular limit problem from the damped wave equation with a power type nonlinearity (NLDW) to the corresponding heat equation (NLH). We call our singular limit problem non-delay limit. We show that the solution of NLDW goes to the one of NLH in [Formula: see text] topology under the both [Formula: see text] regularity solutions. We also obtain the positive convergence rate in the weaker topology [Formula: see text]. Moreover, with restriction of the range of power, if the solution to NLH is global and decays to zero, then we get the global-in-time uniform convergence of the non-delay limit.