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

This paper concerns the asymptotic behaviour of solutions of a linear convolution Volterra summation equation with an unbounded forcing term. In particular, we suppose the kernel is summable and ascribe growth bounds to the exogenous…

We consider a higher-order evolution equation with an inhomogeneous term depending on time and space. We first derive a general criterion for the nonexistence of weak solutions. Next, we study the particular case when the inhomogeneity…

It is well known from the work of [2] that the Fujita phenomenon for reaction-diffusion evolution equations with power nonlinearities does not occur on the hyperbolic space $\mathbb{H}^N$, thus marking a striking difference with the…

In this work, we are interested on the study of the Fujita exponent and the meaning of the blow-up for the Fractional Cauchy problem with the Hardy potential, namely, \begin{equation*} u_t+(-\Delta)^s…

We prove the existence of a critical Fujita exponent for a non-homogeneous semilinear heat equation which involves degenerate coefficients. More precisely, in order to give a rather complete theory, we focus on two types of weights…

This paper deals with an improvement of the "a-priori stability bounds" on the variation of the action variables and on the stability time obtained from a given Birkhoff normal form around the elliptic equilibrium point of an Hamiltonian…

Motivated by the numerical investigation by Aoki et al. [1], we study a rarefied gas flow between two parallel infinite plates of the same temperature governed by the Boltzmann equation with diffuse reflection boundaries, where one plate is…

We consider a class of Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions that describe possible short-range interactions between the binary mixture and the solid boundary. In the presence of surface diffusion on…

We investigate the evolution of the surface of radiating stars by studying the asymptotic behaviour of exact solutions initiated via the stationary boundary condition. This boundary condition leads to a master equation in the form of a…

We study the periodic boundary value problem associated with the second order nonlinear equation \begin{equation*} u'' + ( \lambda a^{+}(t) - \mu a^{-}(t) ) g(u) = 0, \end{equation*} where $g(u)$ has superlinear growth at zero and sublinear…

In this paper, we prove sharp blow-up and global existence results for a time fractional diffusion-wave equation with a nonlinear memory term in a bounded domain, where the fractional derivative in time is taken in the sense of Caputo type.…

We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…

An evolution problem for abstract differential equations is studied. The typical problem is: $$\dot{u}=A(t)u+F(t,u), \quad t\geq 0; \,\, u(0)=u_0;\quad \dot{u}=\frac {du}{dt}\qquad (*)$$ Here $A(t)$ is a linear bounded operator in a Hilbert…

This paper is concerned with a type of nonlinear reaction-diffusion equation, which arises from the population dynamics. The equation includes a certain type reaction term $u^\alpha(1- \sigma \int_{\R^n}u^\beta dx)$ of dimension $n \ge 1$…

In this paper, we obtain the so-called Fujita exponent to the following parabolic system with time-weighted sources and degenerate coefficients $ u_{t}- \mbox{div} ( \omega(x)\nabla { u} )= t^{r} v^{p} $ and $ v_{t}- \mbox{div} (…

In this note we discuss an abstract framework for standard boundary value problems in divergence form with maximal monotone relations as "coefficients". A reformulation of the respective problems is constructed such that they turn out to be…

For the fractional diffusion-wave equation with the Caputo-Dzhrbashyan fractional derivative of order $\alpha \in (1,2)$ with respect to the time variable, we prove an analog of the principle of limiting amplitude (well-known for the wave…

This paper discusses finite time extinction for a perturbed fast diffusion equation with dynamic boundary conditions. The fast diffusion equation has the characteristic property of decay, such as the solution decays to zero in a finite…

In a recent paper we have considered the long time asymptotics of the periodic Toda lattice under a short range perturbation and we have proved that the perturbed lattice asymptotically approaches a modulated lattice. In the present paper…

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.