562 research outputs found
EXPONENTIAL GROWTH OF SOLUTIONS FOR A VARIABLE-EXPONENT FOURTH-ORDER VISCOELASTIC EQUATION WITH NONLINEAR BOUNDARY FEEDBACK
In this paper we study a variable-exponent fourth-order viscoelastic equation of the formin a bounded domain of . Under suitable conditions on variable exponents and initial data, we prove that the solutions will grow up as an exponential function with positive initial energy level. Our result improves and extends many earlier results in the literature such as the on by Mahdi and Hakem (Ser. Math. Inform. 2020, https://doi.org/10.22190/FUMI2003647M)
On a viscoelastic heat equation with logarithmic nonlinearity
This work deals with the following viscoelastic heat equations with logarithmic nonlinearity ut − ∆u + Z t 0 g(t − s)∆u(s)ds = |u| p−2u ln |u|. In this paper, we show the effects of the viscoelastic term and the logarithmic nonlinearity to the asymptotic behavior of weak solutions. Our results extend the results of Peng and Zhou [Appl. Anal. 100(2021), 2804–2824] and Messaoudi [Progr. Nonlinear Differential Equations Appl. 64(2005), 351–356.]
Interior feedback stabilization of wave equations with dynamic boundary delay
In this paper we consider an interior stabilization problem for the wave
equation with dynamic boundary delay.We prove some stability results under the
choice of damping operator. The proof of the main result is based on a
frequency domain method and combines a contradiction argument with the
multiplier technique to carry out a special analysis for the resolvent
Note on Global Regularity for 2D Oldroyd-B Fluids with Diffusive Stress
We prove global regularity of solutions of Oldroyd-B equations in 2 spatial
dimensions with spatial diffusion of the polymeric stresses
Finite-dimensional attractors for the quasi-linear strongly-damped wave equation
We present a new method of investigating the so-called quasi-linear strongly
damped wave equations in bounded 3D domains. This method
allows us to establish the existence and uniqueness of energy solutions in the
case where the growth exponent of the non-linearity is less than 6 and
may have arbitrary polynomial growth rate. Moreover, the existence of a
finite-dimensional global and exponential attractors for the solution semigroup
associated with that equation and their additional regularity are also
established. In a particular case which corresponds to the
so-called semi-linear strongly damped wave equation, our result allows to
remove the long-standing growth restriction .Comment: 36 page
Stability and Well-posedness of a Nonlinear Railway Track Model
Railway tracks rest on a foundation known for exhibiting nonlinear
viscoelastic behavior. Railway track deflections are modeled by a semilinear
partial differential equation. This paper studies the stability of solutions to
this equation in presence of an input. With the aid of a suitable Lyapunov
function, existence and exponential stability of classical solutions is
established for certain inputs. The Lyapunov function is further used to find
an a-priori estimate of the solutions, and also to study the input-to-state
stability (ISS) of mild solutions
- …