Global existence and exponential growth for a viscoelastic wave equation with dynamic boundary conditions

The goal of this work is to study a model of the wave equation with dynamic boundary conditions and a viscoelastic term. First, applying the Faedo-Galerkin method combined with the fixed point theorem, we show the existence and uniqueness of a local in time solution. Second, we show that under some restrictions on the initial data, the solution continues to exist globally in time. On the other hand, if the interior source dominates the boundary damping, then the solution is unbounded and grows as an exponential function. In addition, in the absence of the strong damping, then the solution ceases to exist and blows up in finite time.Comment: arXiv admin note: text overlap with arXiv:0810.101

On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity

We prove global solvability of the third-order in time Jordan-More-Gibson-Thompson acoustic wave equation with memory in $\mathbb{R}^n$, where $n \geq 3$. This wave equation models ultrasonic propagation in relaxing hereditary fluids and incorporates both local and cumulative nonlinear effects. The proof of global solvability is based on a sequence of high-order energy bounds that are uniform in time, and derived under the assumption of an exponentially decaying memory kernel and sufficiently small and regular initial data

Local existence and exponential growth for a semilinear damped wave equation with dynamic boundary conditions

In this paper we consider a multi-dimensional damped semiliear wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. We firstly prove the local existence by using the Faedo-Galerkin approximations combined with a contraction mapping theorem. Secondly, the exponential growth of the energy and the $L^p$ norm of the solution is presented

Local well-posedness of a coupled Westervelt–Pennes model of nonlinear ultrasonic heating

Contains fulltext : 283547.pdf (Publisher’s version ) (Open Access

Global existence and finite time blow-up in a class of stochastic nonlinear wave equations

We consider a stochastic extension of a class of wave equations with nonlinear viscoelastic damping and nonlinear forcing. We show the global existence of the solution of the stochastic equation and, additionally, when the source term dominates the damping term and when the initial data are large enough, we show that the expected value of the L p norm of the solution, blows up in finite time. In the presence of noise, we extend the previously known range of initial data corresponding to blow-up. Furthermore we use a spectral stochastic Galerkin method to perform numerical simulations that verify certain special cases of our theoretical results

Management of spinal dural arterio venous fistula with peri-medullar drainage: Experience of a north-African centre

Introduction: Spinal Dural Arterio Venous Fistula (SDAVF) is an arteriovenous communication on the spinal dura with peri-medullar venous drainage. It is a curable cause of myelopathy and the most common form of spinal arterio venous malformation (AVM). The average age of revelation is the fifth decade; it is a diagnostic and therapeutic emergency. Materials and methods: This is a retrospective study conducted in the neuro surgical department of CHU Bab El Oued in Algiers during a five years time from November 2013 to September 2018. We assessed the clinical status of patients according to the Aminoff-Logue disability score before and after surgery. All patients did a total spine MRI followed by a Medullar angiography which facilitated the pin-pointing of the exact location of the dural fistula. The mean follow-up is 30 months. Results: There were five males and two females, all of them older than 45 years of age. At the admission, patients presented with signs of neurological deficits. After the diagnosis of SDAVF the surgical intervention consisted of a disconnection of the arteriovenous communication by coagulation and section of the fistula at the foot of the vein after a laminectomy. Functional rehabilitation was prescribed for all patients and they were regularly followed-up. Conclusion: Treatment of AVF is surgical or endovascular. Results depend largely on preoperative neurological status