Blowup for nonlinearly damped viscoelastic equations with logarithmic source and delay terms
نویسندگان
چکیده
Abstract In this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to nonlinear damping term instead of strong or linear dissipation, cannot apply concavity method introduced by Levine. Thus, utilizing energy method, show that solutions not only non-positive initial but also some positive blow up at a finite point time.
منابع مشابه
The Nonlinearly Damped Oscillator
We study the large-time behaviour of the nonlinear oscillator mx′′ + f(x′) + k x = 0 , where m, k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f(x′) = A |x′|α−1x′ with α real, A > 0. We characterize the existence and behaviour of fast orbits, i....
متن کاملSemilinear Nonlocal Differential Equations with Delay Terms
The goal of this paper is to obtain the regularity and the existence of solutions of a retarded semilinear differential equation with nonlocal condition by applying Schauder’s fixed point theorem. We construct the fundamental solution, establish the Hölder continuity results concerning the fundamental solution of its corresponding retarded linear equation, and prove the uniqueness of solutions ...
متن کاملBlowup and Asymptotic Stability of Weak Solutions to Wave Equations with Nonlinear Degenerate Damping and Source Terms
This article concerns the blow-up and asymptotic stability of weak solutions to the wave equation utt −∆u + |u|j(ut) = |u|p−1u in Ω× (0, T ), where p > 1 and j′ denotes the derivative of a C1 convex and real value function j. We prove that every weak solution is asymptotically stability, for every m such that 0 < m < 1, p < k + m and the the initial energy is small; the solutions blows up in fi...
متن کاملA Blowup Criterion for Ideal Viscoelastic Flow
We establish an analog of the Beale–Kato–Majda criterion for singularities of smooth solutions of the system of PDE arising in the Oldroyd model for ideal viscoelastic flow. It is well known that smooth solutions of the initial value problem associated with Euler’s equations { ∂tu+ (u · ∇)u = −∇p ∇ · u = 0 , (x, t) ∈ R 3 × (0, T ) (1.1) exist for some finite time T > 0. Here u = u(x, t) ∈ R and...
متن کاملRemarks on Global Existence and Blowup for Damped Nonlinear Schrödinger Equations
We consider the Cauchy problem for the damped nonlinear Schrödinger equations, and prove some blowup and global existence results which depend on the size of the damping coefficient. We also discuss the L concentration phenomenon of blowup solutions in the critical case.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2021
ISSN: ['1687-1839', '1687-1847']
DOI: https://doi.org/10.1186/s13662-021-03469-8