Temporal monotonicity of the solutions of some semilinear parabolic equations with fractional diffusion

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:354

Article; Proceedings Paper

Macias, Siegfried¹  Villa-Morales, Jose² 

[1] Univ Autonoma Aguascalientes, Ctr Ciencias Basicas, Av Univ 940,Ciudad Univ, Aguascalientes 20131, Ags, Mexico

[2] Univ Autonoma Aguascalientes, Dept Matemat & Fis, Av Univ 940,Ciudad Univ, Aguascalientes 20131, Ags, Mexico

关键词: Temporal monotonicity;    Asymptotic behavior;    Positive solutions;    Semilinear parabolic equations;    Fractional diffusion;   

DOI  :  10.1016/j.cam.2018.08.059

来源: Elsevier

【 摘 要 】

Suppose that the functions g, rp and* are nonnegative and satisfy suitable regularity conditions. Then, we prove in this work that the parabolic semilinear problem atu(t, x) =.6c,u(t, x) g(x)f(u(t, x)) + co(x), t > 0, x E R, U(0, X) = Ifr(X), X E R, has a unique positive and time -monotone solution. Here, da is the fractional Laplacian with a E (0, 2], and the source term f is a convex function with f (0) = 0. Moreover, using the temporal monotonicity, we show that the elliptic equation /la v(x) = g(x)f(v(x)) <,o(x), x EIS d, with boundary condition u(x) = 0, has a positive solution. We provide also sufficient conditions for the integrability of both solutions. (C) 2018 Elsevier B.V. All rights reserved.

【 授权许可】

Free