In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut=J∗u−u+G∗(f(u))−f(u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection–diffusion equation ut=Δu+b⋅∇(f(u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection–diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t→∞ when f(u)=|u|q−1u with q>1. We find the decay rate and the first-order term in the asymptotic regime.

Liviu I. Ignat

Julio D. Rossi

Journal of Functional Analysis

《泛函分析杂志》展示了现代泛函分析发挥基本作用的所有科学学科的原创研究论文。发表了各种跨学科领域的科学家的文章。研究领域包括： • 泛函分析的重要应用，包括在其他数学领域的应用 • 泛函分析的新发展 • 对泛函分析中重要问题和挑战的贡献

The Journal of Functional Analysis publishes original research papers that showcase the fundamental role of modern functional analysis across various scientific disciplines. It features articles from scientists in diverse interdisciplinary fields. The areas of research include: • Significant applications of functional analysis in other areas of mathematics • New developments in functional analysis • Contributions to important problems and challenges in functional analysis.

《Journal of Functional Analysis》刊登了现代泛函分析在各科学领域中的原创研究论文，展示了其基本作用。文章涵盖了多个跨学科领域，研究内容包括： • 泛函分析在其他数学领域的重要应用 • 泛函分析的新发展 • 对泛函分析中重要问题和挑战的贡献

Category	Quartile
数学	2
数学, 数学	2

A nonlocal convection–diffusion equation

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