Abstract
In this article, we deal with a strongly damped von Karman equation with variable exponent source and memory effects. We investigate blow-up results of solutions with three levels of initial energy such as non-positive initial energy, certain positive initial energy, and high initial energy. Furthermore, we estimate not only the upper bound but also the lower bound of the blow-up time.
Highlights
1 Introduction In this work, we discuss a viscoelastic von Karman equation with strong damping and variable exponent source terms, t wtt + 2w – h(t – s) 2w(s) ds – wt
It is worthwhile to mention that there is little work concerning global nonexistence of solutions for viscoelastic von Karman equations with variable source effect
We estimate the upper bound and the lower bound of the blow-up time
Summary
We discuss a viscoelastic von Karman equation with strong damping and variable exponent source terms, t wtt + 2w – h(t – s) 2w(s) ds – wt. Messaoudi et al [15] considered wave equations with source and damping terms of variable exponent, wtt – w + a|wt|γ (x)–2wt = b|w|q(x)–2w They obtained the local existence of solutions under appropriate conditions on γ (·) and q(·) by utilizing the Faedo–Galerkin’s technique and the contraction mapping theorem. We refer to a recent work [4] for a nonlinear diffusion system involving variable exponents dependent on spatial and time variables and cross-diffusion terms At this point, it is worthwhile to mention that there is little work concerning global nonexistence of solutions for viscoelastic von Karman equations with variable source effect.
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