Related papers: Stability of semi-wavefronts for delayed reaction-…
This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood…
We perform bifurcation analysis of plane wave solutions in one-dimensional cubic-quintic Ginzburg-Landau equation with delayed feedback. Our study reveals how multistability and snaking behavior of plane waves emerge as time delay is…
We devote this paper to study semi-stable nonconstant radial solutions of $S_k(D^2u) = w(|x|)g(u)$ on the Euclidean space $R^n$. We establish pointwise estimates and necessary conditions for the existence of such solutions (not necessarily…
We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity $\delta^2$ represents the ratio of diffusion coefficients. The fronts…
We study the spectral stability of travelling and stationary front and pulse solutions in a class of degenerate reaction-diffusion systems. We characterise the essential spectrum of the linearised operator in full generality and identify…
In this paper, we answer the question about the criteria of existence of monotone travelling fronts $u = \phi(\nu \cdot x+ct), \phi(-\infty) =0, \phi(+\infty) = \kappa,$ for the monostable (and, in general, non-quasi-monotone) delayed…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
We prove stability results for nonlinear diffusion equations of the porous medium and fast diffusion types with respect to the nonlinearity power $m$: solutions with fixed data converge in a suitable sense to the solution of the limit…
Traveling oscillating fronts (TOFs) are specific waves of the form $U_\star (x,t) = e^{-i \omega t} V_\star(x - ct)$ with a profile $V_{\star}$ which decays at $- \infty$ but approaches a nonzero limit at $+\infty$. TOFs usually appear in…
We refine some previous sufficient conditions for exponential stability of the linear ODE $$ u''+ cu' + (b+a(t))u = 0$$ where $b, c>0$ and $a$ is a bounded nonnegative time dependent coefficient. This allows to improve some results on…
We consider the stability theory of solitary wave solutions for the generalized derivative nonlinear Schr\"odinger equation $$ i\partial_{t}u+\partial_{x}^{2}u+i|u|^{2\sigma}\partial_x u=0, $$ where $1<\sigma<2$. The equation has a…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We study travelling fronts of equations of the form $u_{tt} + \phi(u) u_x = u_{xx} + f(u)$. A criterion for the transition from linear to nonlinear marginal stability is established for positive functions $\phi(u)$ and for any reaction term…
In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow…
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for…
In this paper, we consider the phenomenon of monostable pulsating fronts for multi-dimensional reaction-diffusion-advection systems in periodic media. Recent results have addressed the existence of pulsating fronts and the linear…
The study of resonances (and well-posedness) for complex systems under time-periodic loading is of broad interest in application. The work of Galdi et al.~(2014) connects asymptotic stability of solutions to an unforced Cauchy problem to…
We prove existence and conditional energetic stability of solitary-wave solutions for the two classes of pseudodifferential equations $ u_t+\left(f(u)\right)_x-\left(L u\right)_x=0 $ and $ u_t+\left(f(u)\right)_x+\left(L u\right)_t=0, $…
We prove that every bounded stable solution of \[ (-\Delta)^{1/2} u + f(u) =0 \qquad \mbox{in }\mathbb R^3\] is a 1D profile, i.e., $u(x)= \phi(e\cdot x)$ for some $e\in \mathbb S^2$, where $\phi:\mathbb R\to \mathbb R$ is a nondecreasing…
We establish spectral, linear, and nonlinear stability of the vanishing and slow-moving travelling waves that arise as time asymptotic solutions to the Fisher-Stefan equation. Nonlinear stability is in terms of the limiting equations that…