Blow-up phenomena for a viscoelastic wave equation with strong damping and logarithmic nonlinearity
نویسندگان
چکیده
منابع مشابه
Exponential energy decay and blow-up of solutions for a system of nonlinear viscoelastic wave equations with strong damping
with initial and Dirichlet boundary conditions. We prove that, under suitable assumptions on the functions gi, fi (i = 1, 2) and certain initial data in the stable set, the decay rate of the solution energy is exponential. Conversely, for certain initial data in the unstable set, there are solutions with positive initial energy that blow up in finite time. 2000 Mathematics Subject Classificatio...
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*Correspondence: [email protected] School of Mathematical Sciences, Ocean University of China, Qingdao, P.R. China Abstract This work is concerned with the Dirichlet initial boundary problem for a semilinear viscoelastic wave system with nonlinear weak damping and source terms. For nonincreasing positive functions g and h, we show the finite time blow-up of some solutions whose initial data hav...
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where m, r ≥ 2, and g,h, u0, u1, v0, and v1 are functions to be specified later. This type of problems arises naturally in the theory of viscoelasticity and describes the interaction of two scalar fields (see [1, 2]). The integral terms express the fact that the stress at any instant depends not only on the present value but on the entire past history of strains the material has undergone. In [...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2020
ISSN: 1687-1847
DOI: 10.1186/s13662-020-02694-x