论文标题
由下圆柱布朗尼驱动的随机非线性热和波方程的重新归一化
Renormalization of stochastic nonlinear heat and wave equations driven by subordinate cylindrical Brownian noises
论文作者
论文摘要
在本文中，我们研究了由下属圆柱布朗尼噪声驱动的二维圆环上的随机非线性热方程（SNLH）和随机非线性波方程（SNLW），我们通过圆柱形布朗尼的时间来定义了圆柱形布朗的时间来定义，属于圆柱形运动，属于cadecretagecredecredecrecrepecrecrepecrepecretcrepecrepcretabercreasecrecreascorpercreasecoctActocter。为了构建解决方案，我们引入了合适的重新归一化。对于SNLH，我们不能指望解决方案的时间限制，因为噪声是跳跃类型的。此外，由于解决方案的时间积累性较低，我们只能使用二次非线性为SNLH建立局部良好的结果。另一方面，对于SNLW，这些解决方案具有时间连续性，我们可以为一般多项式非线性展示局部良好性。通过此示例，我们可以看到，在跳跃型情况的单数噪声中，热案例的行为比波壳差。
In this paper, we study the stochastic nonlinear heat equations (SNLH) and stochastic nonlinear wave equations (SNLW) on two-dimensional torus driven by a subordinate cylindrical Brownian noise, which we define by the time-derivative of a cylindrical Brownian motion subordinated to a nondecreasing cadlag stochastic process. To construct the solution, we introduce a suitable renormalization. For SNLH, we cannot expect the time-continuity for the solutions because the noise is jump-type. Moreover, due to the low time-integrability of the solutions, we could establish a local well-posedness result for SNLH only with a quadratic nonlinearity. On the other hand, for SNLW, the solutions have time-continuity and we can show the local well-posedness for general polynomial nonlinearities. Through this example, we can see that the heat case behaves worse than the wave case in the singular noise of jump-type cases.
