The paper deals with non-classical initial-boundary value problems for parabolic equations with a fractional Laplacian. We study the existence and uniqueness of a mild solution to our problem. The continuous dependence of the solution on the given data is shown and the ill-posedness of the mild solution at t = 0 is also considered. In order to avoid such ill-posedness, we construct a regularized solution using the Fourier truncation method. An $L^p$ error estimate and the convergence rate between the regularized solution and the exact solution are obtained.

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关于具有分数拉普拉斯和积分条件的非线性抛物方程

本文处理具有分数拉普拉斯算子的抛物线方程的非经典初始边界值问题。我们研究问题的温和解决方案的存在性和唯一性。 显示了解对给定数据的连续依赖性，并且还考虑了t = 0时温和解的不适定性。为了避免这种不适定性，我们使用傅里叶截断方法构造了一个正则化解。一个${\mathrm{大号}}^p$得到了正则化解与精确解之间的误差估计和收敛速度。