Related papers: Evolution equations involving nonlinear truncated …
Particles subject to weak contact interactions in a finite-size lattice tend to thermalise. The Hamiltonian evolution ensures energy conservation and the final temperature is fully determined by the initial conditions. In this work we show…
In the first part of this work we show the convergence with respect to an asymptotic parameter {\epsilon} of a delayed heat equation. It represents a mathematical extension of works considered previously by the authors [Milisic et al. 2011,…
Deterministic and stochastic coupled oscillators with inertia are studied on the rectangular lattice under the shear-velocity boundary condition. Our coupled oscillator model exhibits various nontrivial phenomena and there are various…
This paper concerns the finite-time blow-up and asymptotic behaviour of solutions to nonlinear Volterra integrodifferential equations. Our main contribution is to determine sharp estimates on the growth rates of both explosive and…
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…
For heat flux $q$ and temperature $T$ we introduce a modified Fourier--Cattaneo law $q_t+ l \frac{q}{t}= - kT_x .$ The consequence of it is a non-autonomous telegraph-type equation. % $\epsilon S_{tt} + \frac{a}{t} S_t = S_{xx}$ . This…
Large time behavior of solutions to abstract differential equations is studied. The corresponding evolution problem is: $$\dot{u}=A(t)u+F(t,u)+b(t), \quad t\ge 0; \quad u(0)=u_0. \qquad (*)$$ Here $\dot{u}:=\frac {du}{dt}$, $u=u(t)\in H$,…
Relations similar to work and exchange fluctuations have been recently derived for open systems dynamically evolving in the presence of an ancilla. Extending these relations and constructing a non-equilibrium Helmholtz equation we derive a…
Heat conduction in three-dimensional nonlinear lattices is investigated using a particle dynamics simulation. The system is a simple three-dimensional extension of the Fermi-Pasta-Ulam $\beta$ (FPU-$\beta$) nonlinear lattices, in which the…
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness of solutions…
In this work, we perform a detailed study of heat transport in one dimensional long-ranged anharmonic oscillator systems, such as the long-ranged Fermi-Pasta-Ulam-Tsingou model. For these systems, the long-ranged anharmonic potential decays…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
This paper investigates the initial boundary value problem of a finitely degenerate semilinear pseudo-parabolic equation associated with H\"{o}rmander's operator. Based on the global existence of solutions in previous literature, the…
We consider an abstract nonlinear second order evolution equation, inspired by some models for damped oscillations of a beam subject to external loads or magnetic fields, and shaken by a transversal force. When there is no external force,…
We develop the laws of thermodynamics in terms of general exponential families. By casting learning (log-loss minimization) problems in max-entropy and statistical mechanics terms, we translate thermodynamics results to learning scenarios.…
Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetimes. We treat the so-called heatlike case where the critical exponent is affected by…
This paper proves the local well posedness of differential equations in metric spaces under assumptions that allow to comprise several different applications. We consider below a system of balance laws with a dissipative non local source,…
We develop a variational approach in order to study the qualitative properties of non-autonomous parabolic equations. Based on the method of product integrals, we discuss long-time behavior, invariance properties, and ultracontractivity of…
We investigate the Cauchy problem for a heat equation involving a fractional harmonic oscillator and an exponential nonlinearity. We establish local well-posedness within the appropriate Orlicz spaces. Through the examination of small…
In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations. We establish qualitative results on the existence, nonexistence or the uniqueness of…