论文标题
在调制空间中与分数赫米特操作员相关的非线性热方程的局部良好性
On the local well-posedness of the nonlinear heat equation associated to the fractional Hermite operator in modulation spaces
论文作者
论文摘要
在本说明中，我们考虑了与分数HERMITE操作员$ H^β=（ - δ+| x |^2）^β$，$ 0 <β\ leq 1 $相关的非线性热方程。我们在调制空间的框架中显示了相关的cauchy问题的局部解决性。结果是通过结合微局部和时频分析的工具获得的。作为副产品，我们计算了pseudodifferential运算符的Gabor矩阵，其中hörmander类$ s^m_ {0,0,0} $，$ m \ in \ MATHCAL {r} $。
In this note we consider the nonlinear heat equation associated to the fractional Hermite operator $H^β=(-Δ+|x|^2)^β$, $0<β\leq 1$. We show the local solvability of the related Cauchy problem in the framework of modulation spaces. The result is obtained by combining tools from microlocal and time-frequency analysis. As a byproduct, we compute the Gabor matrix of pseudodifferential operators with symbols in the Hörmander class $S^m_{0,0}$, $m\in\mathcal{R}$.
