Related papers: A striking correspondence between the dynamics gen…
The evolution equations of Einstein's theory and of Maxwell's theory---the latter used as a simple model to illustrate the former--- are written in gauge covariant first order symmetric hyperbolic form with only physically natural…
We establish that the elliptic equation $\Delta u+f(x,u)+g(| x|)x\cdot \nabla u=0$, where $x\in\mathbb{R}^{n}$, $n\geq3$, and $| x|>R>0$, has a positive solution which decays to 0 as $| x|\to +\infty$ under mild restrictions on the…
Here is constructed a heuristic, first-order differential equation for the electromagnetic field in the vacuum, based on a phenomenological \textsl{ad hoc} argument. The formal similarity between this \textsl{ad hoc} wave equation and the…
The notion of fractional dynamics is related to equations of motion with one or a few terms with derivatives of a fractional order. This type of equation appears in the description of chaotic dynamics, wave propagation in fractal media, and…
The equivalence between theories depending on the derivatives of $R$, i.e. $f\left( R,\nabla R,...,\nabla^{n}R\right) $, and scalar-multi-tensorial theories is verified. The analysis is done in both metric and Palatini formalisms. It is…
We discuss the occurrence of positive solutions which decay to 0 as $| x|\to+\infty$ to the differential equation $\Delta u+f(x,u)+g(| x|)x\cdot\nabla u=0$, $| x|>R>0$, $x\in\mathbb{R}^{n}$, where $n\geq 3$, $g$ is nonnegative valued and…
Scalar fields coupled to dark matter by conformal or disformal transformations give rise to a general class of scalar-tensor theories which leads to a rich phenomenology in a cosmological setting. While this possibility has been studied…
We investigate the problem $$ \left\{ \begin{array}{ll} -\Delta_p u = g(u)|\nabla u|^p + f(x,u) \ & \mbox{in} \ \ \Omega, \ \ \\ u>0 \ &\mbox{in} \ \ \Omega, \ \ u = 0 \ &\mbox{on} \ \ \partial\Omega, \end{array} \right. \leqno{(P)} $$ in a…
This paper is concerned with longtime dynamics of semilinear Lam\'e systems $$ \partial^2_t u - \mu \Delta u - (\lambda + \mu) \nabla {\rm div} u + \alpha \partial_t u + f(u) = 0, $$ defined in bounded domains of $\mathbb{R}^3$ with…
The strange behaviour of the universe's dark sector offers us the flexibility to address cosmological problems with different approaches. Using this flexibility, we consider a possible exchange of energy among the dark sector components as…
In this paper we establish compactness results of multiscale and very weak multiscale type for sequences bounded in $L^{2}(0,T;H_{0}^{1}(\Omega ))$, fulfilling a certain condition. We apply the results in the homogenization of the parabolic…
The gravitational self-force (GSF) and post-Newtonian (PN) schemes are complementary approximation methods for modelling the dynamics of compact binary systems. Comparison of their results in an overlapping domain of validity provides a…
There often appear coherently oscillating scalar fields in particle physics motivated cosmological scenarios, which may have rich phenomenological consequences. Scalar fields should somehow interact with background thermal bath in order to…
The answers for Feynman diagrams satisfy various kinds of differential equations -- which is not a surprise, because they are defined as Gaussian correlators, possessing a vast variety of Ward identities and superintegrability properties.…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
We bound the difference between solutions $u$ and $v$ of $u_t = a\Delta u+\Div_x f+h$ and $v_t = b\Delta v+\Div_x g+k$ with initial data $\phi$ and $ \psi$, respectively, by $\Vert u(t,\cdot)-v(t,\cdot)\Vert_{L^p(E)}\le A_E(t)\Vert…
The problem of specification of self-adjoint operators corresponding to singular bilinear forms is very important for applications, such as quantum field theory and theory of partial differential equations with coefficient functions being…
We consider the homogeneous Dirichlet problem for an elliptic equation driven by a linear operator with discontinuous coefficients and having a subquadratic gradient term. This gradient term behaves as $g(u)|\nabla u|^q$, where $1<q<2$ and…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…
Three types of equations of mathematical physics, namely, the equations, which describe any physical processes, the equations of mechanics and physics of continuous media, and field-theory equations are studied in this paper. In the first…