分形Hamilton Jacobi KPZ方程
Fractal Hamilton-Jacobi-KPZ equations
摘要：
本文导出了$u_t=Łu \pm|\nabla u|^q$形式的非线性和非线性发展方程，其中$Ł$是代表Lévy随机过程的无穷小生成元的伪微分算子，作为连续布朗扩散表面输运被随机跳跃机制增强的情况下生长界面的模型。本文的目的是研究这个方程的解的性质，从“扩散”的线性和“双曲”的非线性项，提出了在整个空间$\bbfR^N$的强度之间的相互作用，并补充了非负的，有界的，充分正则的初始条件。
英文摘要：
Nonlinear and nonlinear evolution equations of the form $u_t=Łu \pm|\nabla u|^q$, where $Ł$ is a pseudodifferential operator representing the infinitesimal generator of a Lévy stochastic process, have been derived as models for growing interfaces in the case when the continuous Brownian diffusion surface transport is augmented by a random hopping mechanism. The goal of this paper is to study properties of solutions to this equation resulting from the interplay between the strengths of the "diffusive" linear and "hyperbolic" nonlinear terms, posed in the whole space $\bbfR^N$, and supplemented with nonnegative, bounded, and sufficiently regular initial conditions.
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