相关论文: A note on time-asymptotic bounds with a sharp alge…

In this Note, we describe the stationary equilibria and the asymptotic behaviour of an heterogeneous logistic reaction-diffusion equation under the influence of autonomous or time-periodic forcing terms. We show that the study of the…

In this paper, the global-in-time $ L^2 $-solvability of the initial-boundary value problem for differential inclusions of doubly-nonlinear type, which arises from fracture mechanics, is proved. This problem is not covered by general…

In this paper, we consider the backward problem for fractional in time evolution equations $\partial_t^\alpha u(t)= A u(t)$ with the Caputo derivative of order $0<\alpha \le 1$, where $A$ is a self-adjoint and bounded above operator on a…

In this paper, we numerically address the inverse problem of identifying a time-dependent coefficient in the time-fractional diffusion equation. An a priori estimate is established to ensure uniqueness and stability of the solution. A fully…

In this paper we consider the blow-up problem for a mixed local-nonlocal diffusion operator, \[ u_t=a\Delta u -b(-\Delta)^s u+u^p. \] We show that the Fujita exponent is given by the nonlocal part, $p_F=1+2s/N$. We also determinate, in some…

We investigate whether an accelerating universe can be realized as an asymptotic late-time solution of FLRW-cosmology with multi-field multi-exponential potentials. Late-time cosmological solutions exhibit a universal behavior which enables…

We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…

In this paper, it is proved that, in a dual context, asymptotic expansions of ordinary linear time-differential equations which possess limiting equations to their limiting equations might be obtained by first discretizing them and then…

In the present work, a new time-dependent exchange theory is presented wherein the symmetry constraints, on a multi-electron wavefunction, are properly accounted for. In so doing, the equations of motion, incorporating the required…

In this paper, we show global existence and non-existence results for the heat equation with some of the squares of smooth vector fields on $\Rn$ satisfying H\"{o}rmander's rank condition with a non-linearity of the form $f(u)$, where $f$…

In this paper, we study a critical exponent to the semilinear heat equation with forcing term on Heisenberg group. Our technique of proof is based on methods of nonlinear capacity estimates specifically adapted to the nature of the…

In this paper we investigate the long time behavior of solutions to fractional in time evolution equations which appear as results of random time changes in Markov processes. We consider inverse subordinators as random times and use the…

The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…

In this paper, we consider fractional parabolic equation of the form $ \frac{\partial u}{\partial t}=-(-\Delta)^{\frac{\alpha}{2}}u+u\dot W(t,x)$, where $-(-\Delta)^{\frac{\alpha}{2}}$ with $\alpha\in(0,2]$ is a fractional Laplacian and…

In this paper we are concerned with the asymptotic behavior of nonautonomous fractional approximations of oscillon equation $$ u_{tt}-\mu(t)\Delta u+\omega(t)u_t=f(u),\ x\in\Omega,\ t\in\mathbb{R}, $$ subject to Dirichlet boundary condition…

In this paper we study the asymptotic behavior of a very fast diffusion PDE in 1D with periodic boundary conditions. This equation is motivated by the gradient flow approach to the problem of quantization of measures introduced in…

Taking into account the asymptotic behavior of some Wright functions and the existence of bounds for the Mainardi and the Wright function $W(-x,\frac{\alpha}{2}, 1)$ in $\mathbb{R}^+$ , three different initial-boundary-value problems for…

In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…

We consider non-negative solutions of the fast diffusion equation $u_t=\Delta u^m$ with $m \in (0,1)$, in the Euclidean space R^d, d?3, and study the asymptotic behavior of a natural class of solutions, in the limit corresponding to…

This paper extends the weak solution theory for the 3D Navier-Stokes equations of Barker, Seregin and Sverak from a critical setting to a supercritical setting making sure to include a useful a priori energy bound as well as a statement…