论文标题
随着收获的非局部空间异质逻辑方程的研究
A study of nonlocal spatially heterogeneous logistic equation with harvesting
论文作者
论文摘要
我们研究了一类具有收获项的非局部反应扩散方程，其中非局部操作员由laplacian的伯恩斯坦功能给出。特别是，它包括分数拉普拉斯，分数相对论操作员，不同顺序的分数拉普拉奇人的总和。我们研究了稳态方程解决方案的存在，独特性和多重性结果。我们还考虑了抛物线派对应物，并建立了长期渐近解决方案的方法。我们的证明技术依赖于分析和概率论证。
We study a class of nonlocal reaction-diffusion equations with a harvesting term where the nonlocal operator is given by a Bernstein function of the Laplacian. In particular, it includes the fractional Laplacian, fractional relativistic operators, sum of fractional Laplacians of different order etc. We study existence, uniqueness and multiplicity results of the solutions to the steady state equation. We also consider the parabolic counterpart and establish the long time asymptotic of the solutions. Our proof techniques rely on both analytic and probabilistic arguments.
