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The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested…
We find integrability conditions on the initial data $f$ for the existence of solutions of the Heat problem on the Heisenberg group. From this result we characterize the weighted Lebesgue spaces for which the solutions exists a.e. when the…
Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector…
Asymptotic expansions as well as necessary and sufficient conditions are provided for the pointwise convergence of the spherical partial integrals of the associated Fourier transforms on the real hyperbolic space. The proposed method…
The Hilbert spaces for stable scattering states and particles are determined by the representations of the characterizing Euclidean and Poincar\'e group and given, respectively, by the square integrable functions on the momentum 2-spheres…
We discuss ordinary differential equations with delay and memory terms in Hilbert spaces. By introducing a time derivative as a normal operator in an appropriate Hilbert space, we develop a new approach to a solution theory covering…
The existence and uniqueness of solution to a one-dimensional hyperbolic integro-differential problem arising in viscoelasticity is here considered. The kernel, in the linear viscoelasticity equation, represents the relaxation function…
We study kernel functions, and associated reproducing kernel Hilbert spaces $\mathscr{H}$ over infinite, discrete and countable sets $V$. Numerical analysis builds discrete models (e.g., finite element) for the purpose of finding…
We prove that a large class of parabolic final value problems is well posed.This results via explicit Hilbert spaces that characterise the data yielding existence, uniqueness and stability of solutions. This data space is the graph normed…
This paper considers the existence of a global-in-time strong solution to the heat equations in the two half spaces $\mathbb{R}^3_+(=\mathbb{R}^2 \times (0,\infty))$, $\mathbb{R}^3_-(= \mathbb{R}^2 \times (-\infty ,0))$, and the interface…
We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order…
We study stochastic convolutions providing by fundamental solutions of a class of integrodifferential equations which interpolate the heat and the wave equations. We give sufficient condition for the existence of function--valued…
We present some analytical solutions to the Einstein equations, describing radiating collapsing spheres in the diffusion approximation. Solutions allow for modeling physical reasonable situations. The temperature is calculated for each…
Large-time behaviour of solutions to stochastic evolution equations driven by two-sided regular Volterra processes is studied. The solution is understood in the mild sense and takes values in a separable Hilbert space. Sufficient conditions…
We study general Hilbert modules over the disc algebra and exhibit necessary spectral conditions for the vanishing of certain associated extension groups. In particular, this sheds some light on the problem of identifying the projective…
This paper studies existence and uniqueness of solutions to generalized Volterra integral equations. Since our proof for existence and uniqueness does not make use of Banach fixed point theorem unlike the previous papers focused on this…
We establish the $L^2$-solvability of Dirichlet, Neumann and regularity problems for divergence-form heat (or diffusion) equations with H\"older-continuous diffusion coefficients, on bounded Lipschitz domains in $\mathbb{R}^n$. This is…
We propose a thermodynamically consistent general-purpose model describing diffusion of a solute or a fluid in a solid undergoing possible phase transformations and damage, beside possible visco-inelastic processes. Also heat…
One method to determine whether or not a system of partial differential equations is consistent is to attempt to construct a solution using merely the "algebraic data" associated to the system. In technical terms, this translates to the…
In this paper we study removable singularities for solutions of the fractional heat equation in time varying domains. We introduce associated capacities and we study some of its metric and geometric properties.