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Erhan Pişkin
Public Documents
4
General decay and blow up of solutions for a variable-exponent viscoelastic double-Ki...
Mohammad Shahrouzi
and 2 more
November 17, 2021
In this paper we consider a viscoelastic double-Kirchhoff type wave equation of the form $$ u_{tt}-M_{1}(\|\nabla u\|^{2})\Delta u-M_{2}(\|\nabla u\|_{p(x)})\Delta_{p(x)}u+(g\ast\Delta u)(x,t)+\sigma(\|\nabla u\|^{2})h(u_{t})=\phi(u), $$ where the functions $M_{1},M_{2}$ and $\sigma, \phi$ are real valued functions and $(g\ast\nabla u)(x,t)$ is the viscoelastic term which are introduced later. Under appropriate conditions for the data and exponents, the general decay result and blow-up of solutions are proved with positive initial energy. This study extends and improves the previous results in the literature to viscoelastic double-Kirchhoff type equation with degenerate nonlocal damping and variable-exponent nonlinearities.
Blow up of solutions for a nonlinear Petrovsky type Equation with Logarithmic Nonline...
Nazlı IRKIL
and 1 more
November 02, 2020
The aim of this paper is to investigate the initial boundary value problem of nonlinear viscoelastic Petrovsky type equation with logarithmic nonlinearity. We derive the blow up results by the combination of the perturbation energy method, concavity method and differantial-integral inequality technique.
Blow up and asymptotic behavior of solutions for a p(x)-Laplacian equations with dela...
Stanilslav Antontsev
and 3 more
January 04, 2021
In this paper, we consider a nonlinear p .x/Laplacian equation with delay of time and variable exponents. Firstly, we prove the blow up of solutions. Then, by applying an integral inequality due to Komornik, we obtain the decay result. These results improve and extend earlier results in the literature.
Local existence and blow up of solutions to a Petrovsky equation with variable-expone...
Jorge Ferreira
and 1 more
March 17, 2020
In this paper, we consider a nonlinear plate (or beam) Petrovsky equation with strong damping and source terms with variable exponents. The exponents of nonlinearity _p_(⋅) and _q_(⋅) are given functions. By using the Banach contraction mapping principle the local existence of a weak solutions is established under suitable assumptions on the variable exponents _p_ and _p_. We also show a finite time blow up result for the solutions with negative initial energy.