相关论文: On the Gevrey ultradifferentiability of weak solut…

Analytic smooth solutions of a general, strongly parabolic semi-linear Cauchy problem of $2m$-th order in $\mathbb{R}^N\times (0,T)$ with analytic coefficients (in space and time variables) and analytic initial data (in space variables) are…

In this paper, we would like to consider the Cauchy problem for a multi-component weakly coupled system of semi-linear $\sigma$-evolution equations with double dissipation for any $\sigma\ge 1$. The first main purpose is to obtain the…

We consider an equation of the form $y'(t) + Ay(t) = 0, \ t \in [0, \infty)$, where $A$ is a nonnegative self-adjoint operator in a Hilbert space. We give direct and inverse theorems on approximation of solutions of this equation with its…

We investigate the effect of nonlocal conditions expressed by linear continuous mappings over the hypotheses which guarantee the existence of global mild solutions for functional-differential equations in a Banach space. A progressive…

This paper is concerned with the inverse spectral problem for the third-order differential equation with distribution coefficient. The inverse problem consists in the recovery of the differential expression coefficients from the spectral…

We present a spectral mapping theorem for semigroups on any Banach space $E$. From this, we obtain a characterization of exponential dichotomy for nonautonomous differential equations for $E$-valued functions. This characterization is given…

It is well known that the non-autonomous scalar differential equation of evolution has a unique solution given by an elementary exponential function. In general there is no such analogous solution to the corresponding non-autonomous…

In this article, we consider the linear operator equation in a Banach space. The relative perturbation of the solution x corresponding to the perturbation of y, the perturbation of A and the perturbation of both A, y are characterized from…

We consider evolution differential equations in Fr\'echet spaces that possess unconditional Schauder basis and construct a version of the majorant functions method to obtain existence theorems for Cauchy problems. Applications to PDE and…

Geodesic contraction in vector-valued differential equations is readily verified by linearized operators which are uniformly negative-definite in the Riemannian metric. In the infinite-dimensional setting, however, such analysis is…

A random vector ${\bf X}$ is weakly stable iff for all $a,b \in \mathbb{R}$ there exists a random variable $\Theta$ such that $a{\bf X} + b {\bf X}' \stackrel{d}{=} {\bf X} \Theta$, where $X'$ is an independent copy of $X$ and $\Theta$ is…

Let $E$ and $G$ be two Banach function spaces, let $T \in \mathcal{L}(E,Y)$, and let ${\langle X,Y \rangle}$ be a Banach dual pair. In this paper we give conditions for which there exists a (necessarily unique) bounded linear operator…

Complex demodulation of evolutionary spectra is formulated as a two-dimensional kernel smoother in the time-frequency domain. In the first stage, a tapered Fourier transform, $y_{nu}(f,t)$, is calculated. Second, the log-spectral estimate,…

For a scalar evolution equation $u_t=K(t,x,u,u_x,\ldots, u_n), n\geq 2$ the cohomology spaces $H^{1,s}({\mathcal R}^\infty)$ vanishes for $s\geq 3$ while the space $H^{1,2}({\mathcal R}^\infty)$ is isomorphic to the space of variational…

We define new symbol classes for pseudodifferntial operators and investigate their pseudodifferential calculus. The symbol classes are parametrized by commutative convolution algebras. To every solid convolution algebra over a lattice we…

We consider an evolution equation with the regularized fractional derivative of an order $\alpha \in (0,1)$ with respect to the time variable, and a uniformly elliptic operator with variable coefficients acting in the spatial variables.…

Smoothing (and decay) spacetime estimates are discussed for evolution groups of self-adjoint operators in an abstract setting. The basic assumption is the existence (and weak continuity) of the spectral density in a functional setting.…

We study conditions for the well-posedness of nonautonomous perturbation of evolution equations of the form \[ u'(t)=(A+B(t))u(t), \quad t \in [a,b], \] where $A$ generates a $\mathrm{C}_0$-semigroup $\left (T(t)\right )_{t\ge 0}$ with $\|…

We generalize the results for Banach algebras of pseudodifferential operators obtained by Gr\"ochenig and Rzeszotnik in [24] to quasi-algebras of Fourier integral operators. Namely, we introduce quasi-Banach algebras of symbol classes for…

A bounded operator $T$ in a Banach space $X$ is said to satisfy the essential descent spectrum equality, if the descent spectrum of $T$ as an operator on $X$ coincides with the essential descent spectrum of $T$. In this note, we give some…