On stabilization of solutions of higher order evolution inequalities

Article type: Research Article

Authors: Kon’kov, Andrej^{a; *} | Shishkov, Andrey^{b; c}

Affiliations: [a] Department of Differential Equations, Faculty of Mechanics and Mathematics, Moscow Lomonosov State University, Russia. E-mail: [email protected] | [b] Center of Nonlinear Problems of Mathematical Physics, RUDN University, Russia | [c] Institute of Applied Mathematics and Mechanics of NAS of Ukraine, Ukraine. E-mail: [email protected]

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We obtain sharp conditions guaranteeing that every non-negative weak solution of the inequality ∑|α|=m∂αaα(x,t,u)−ut⩾f(x,t)g(u)in R+n+1=Rn×(0,∞),m,n⩾1, stabilizes to zero as t→∞. These conditions generalize the well-known Keller–Osserman condition on the growth of the function g at infinity.

Keywords: Higher order evolution inequalities, nonlinearity, stabilization

DOI: 10.3233/ASY-191522

Journal: Asymptotic Analysis, vol. 115, no. 1-2, pp. 1-17, 2019