具有反常扩散的对流方程解的远场渐近性
Far field asymptotics of solutions to convection equation with anomalous diffusion
摘要：
研究了守恒律方程$\partial_t u+(-Δ)^{α/2}u+\nabla \cdot f(u)=0$的初值问题，在自然多项式增长条件下，对$α\in (1,2)$的非线性项进行了研究.我们发现这个方程的解对应于初始条件的渐近展开式为$|x|\to \infty$，在无穷远处衰减得足够快。
英文摘要：
The initial value problem for the conservation law $\partial_t u+(-Δ)^{α/2}u+\nabla \cdot f(u)=0$ is studied for $α\in (1,2)$ and under natural polynomial growth conditions imposed on the nonlinearity. We find the asymptotic expansion as $|x|\to \infty$ of solutions to this equation corresponding to initial conditions, decaying sufficiently fast at infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
