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In this paper, we give a small data blow-up result for the one-dimensional semilinear wave equation with damping depending on time and space variables. We show that if the damping term can be regarded as perturbation, that is, non-effective…
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We construct the unperturbed limit cycle analytically, and are…
This paper is concerned with approximation of blow-up phenomena in nonlinear parabolic problems. We consider the equation u_t = u_xx +|u|^p -b(x)|u_x|^q in a bounded domain, we study the behavior of the semidiscrete problem. Under some…
In this work, we study the behavior of blow-up solutions to the multidimensional restricted Euler--Poisson equations which are the localized version of the full Euler--Poisson system. We provide necessary conditions for the existence of…
In this paper, we consider a blow-up solution for the complex-valued semilinear wave equation with power nonlinearity in one space dimension. We first characterize all the solutions of the associated stationary problem as a two-parameter…
We study positive blowing-up solutions of the system: $$u_{t}-\delta\Delta u=v^p,\,\,\, v_{t}-\Delta v=u^{q},$$ as well as of some more general systems. For any $p,\,q>1$, we prove single-point blow-up for any radially decreasing, positive…
In this paper, we investigate the initial boundary value problem of the following nonlinear extensible beam equation with nonlinear damping term $$u_{t t}+\Delta^2 u-M\left(\|\nabla u\|^2\right) \Delta u-\Delta u_t+\left|u_t\right|^{r-1}…
The integrate and fire equation is a classical model for neural assemblies which can exhibit finite time blow-up. A major open problem is to understand how to continue solutions after blow-up. Here we study an approach based on random…
We consider a typical class of systems with delayed nonlinearity, which we show to exhibit chaotic diffusion. It is demonstrated that a periodic modulation of the time-lag can lead to an enhancement of the diffusion constant by several…
In this paper, stability analysis of time delay systems is considered based on decomposition of the systems to subsystems. The decomposition process needs matrices of these systems to be simultaneously block triangularize. We show that a…
For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The…
In this paper, blow-up solutions of autonomous ordinary differential equations (ODEs) which are unstable under perturbations of initial points, referred to as saddle-type blow-up solutions, are studied. Combining dynamical systems machinery…
The paper investigates a class of a semilinear wave equation with time-dependent damping term ($-\frac{1}{{(1+t)}^{\beta}}\Delta u_t$) and a nonlinearity $|u|^p$. We will show the influence of the the parameter $\beta$ in the blow-up…
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of…
In this paper, we consider a semilinear parabolic equation with nonlinear nonlocal Neumann boundary condition and nonnegative initial datum. We first prove global existence results. We then give some criteria on this problem which determine…
In this paper we consider a porous-elastic system consisting of nonlinear boundary/interior damping and nonlinear boundary/interior sources. Our interest lies in the theoretical understanding of the existence, finite time blow-up of…
Predictor-based stabilization results are provided for nonlinear systems with input delays and a compact absorbing set. The control scheme consists of an inter-sample predictor, a global observer, an approximate predictor, and a nominal…
We consider the elliptic-elliptic Davey-Stewartson system in the three-dimensional Euclidean space, and we give sufficient conditions for the existence of finite time blow-up solutions in non-isotropic spaces. The proof is based on some…
The Miles-Krasnopolskaya system is considered, which is used to study the nonlinear interaction of a tank with a liquid and the source of excitation of its oscillations. Additionally, delay time of impulse from the source of excitation of…
In this paper we prove the blow-up theorem in the critical case for weakly coupled systems of semilinear wave equations in high dimensions. The upper bound of the lifespan of the solution is precisely clarified.