Related papers: Long-time behaviour for a non-autonomous Klein-Gor…
In this paper, we consider an autonomous semi-dynamical system driven by semilinear time-nonlocal evolution equations, these type equations are used to describe the Rayleigh-Stokes problem for a non-Newtonain fluid to a generalized second…
In this article we consider one-dimensional scalar quasilinear Klein--Gordon equations with general nonlinearities, on both $\mathbb{R}$ and $\mathbb{T}$. By employing a refined modified-energy framework of Ifrim and Tataru, we investigate…
The purpose of this paper is to investigate the time behavior of the solution of a weighted $p$-Laplacian evolution equation, given by \begin{align} \label{eveq} \begin{cases} u_{t} = \text{div} \left(\gamma |\nabla u|^{p-2}\nabla u \right)…
We consider the Keller-Segel-type migration-consumption system involving signal-dependent motilities, $$\left\{ \begin{array}{l} u_t = \Delta \big(u\phi(v)\big), \\[1mm] v_t = \Delta v-uv, \end{array} \right. \qquad \qquad$$ in smoothly…
This work, Part II, together with its companion Part I develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past states.…
In this paper we consider the following nonlocal autonomous evolution equation in a bounded domain $\Omega$ in $\mathbb{R}^N$ \[ \partial_t u(x,t) =- h(x)u(x,t) + g \Big(\int_{\Omega} J(x,y)u(y,t)dy \Big) +f(x,u(x,t)) \] where $h\in…
We investigate the non-equilibrium properties of an N-component scalar field theory. The time evolution of the correlation functions for an arbitrary ensemble of initial conditions is described by an exact functional differential equation.…
We deal with the existence of solutions having L2 regularity for a class of non autonomous evolution equations. Associated with the equation, a general non local condition is studied. The technique we used combines a finite dimensional…
We consider the nonlinear Klein Gordon Maxwell system on four dimensional Minkowski space-time. For appropriate nonlinearities the system admits soliton solutions which are gauge invariant generalizations of the non-topological solitons…
We present a local framework for investigating non-unitary evolution groups pertinent to effective field theories in general semi-classical spacetimes. Our approach is based on a rigorous local stability analysis of the algebra of…
We investigate the long-time behavior of global solutions to the energy critical heat equation in $R^5$ \begin{equation*} \begin{cases} \pp_t u=\Delta u+|u|^{\frac{4}{3}} u ~&\mbox{ in }~ R^5 \times (t_0,\infty), u(\cdot,t_0)=u_0~&\mbox{ in…
In this paper we study the evolution problem \[ \left\lbrace\begin{array}{ll} u_t (x,t)- \lambda_j(D^2 u(x,t)) = 0, & \text{in } \Omega\times (0,+\infty), \\ u(x,t) = g(x,t), & \text{on } \partial \Omega \times (0,+\infty), \\ u(x,0) =…
We investigate nonlinear dynamics near an unstable constant equilibrium in the classical Keller-Segel model. Given any general perturbation of magnitude $\delta$, we prove that its nonlinear evolution is dominated by the corresponding…
A non-periodic version of the one-predator two-prey system model presented in [L.T.H. Nguyen, Q.H. Ta, T.V. T\d{a}, Existence and stability of periodic solutions of a Lotka-Volterra system, SICE International Symposium on Control Systems,…
This paper is a detailed and self-contained study of the stability properties of periodic traveling wave solutions of the nonlinear Klein-Gordon equation $u_{tt}-u_{xx}+V'(u)=0$, where $u$ is a scalar-valued function of $x$ and $t$, and the…
Modulation spaces have received considerable interest recently as it is the natural function spaces to consider low regularity Cauchy data for several nonlinear evolution equations. We establish global well-posedness for 3D…
For general nonlinear Klein-Gordon equations with dissipation we show that any finite energy radial solution either blows up in finite time or asymptotically approaches a stationary solution in $H^1\times L^2$. In particular, any global…
Given any $\mu_1, \mu_2\in {\mathbb C}$ and $\alpha >0$, we prove the local existence of arbitrarily smooth solutions of the nonlinear Klein-Gordon equation $\partial_{ tt } u - \Delta u + \mu_1 u = \mu_2 |u|^\alpha u$ on ${\mathbb R}^N$,…
The paper investigates the existence and upper semicontinuity of uniform attractors of the perturbed non-autonomous Kirchhoff wave equations with strong damping and supercritical nonlinearity: $u_{tt}-\Delta u_{t}-(1+\epsilon\|\nabla…
We prove maximal $L^p$-regularity for the stochastic evolution equation \[\{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}.\] under the assumption that $A$ is a sectorial…