相关论文: Existence and qualitative properties of kinetic fu…
The KdV-Burgers equation is a canonical model describing the interplay between nonlinearity, viscosity and dispersion, and it admits viscous-dispersive shocks as traveling wave solutions. In this paper, we establish an $L^2$-contraction…
In this paper, we study the existence of traveling wave solutions and the spreading speed for the solutions of an age-structured epidemic model with nonlocal diffusion. Our proofs make use of the comparison principles both to construct…
The existence of normal deterministic diffusion in dynamical systems with a two-dimensional phase space tiled by regular triangles (or their unions into regular hexagons) is proven.
The development of a coherent conceptual basis for the treatment of non-linear microscopic phenomena, such as, hydrodynamic interaction, finite extensibility, excluded volume and internal viscosity, in molecular theories of dilute polymer…
The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints, which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane…
This paper studies regularity property of the value function for an infinite-horizon discounted cost impulse control problem, where the underlying controlled process is a multidimensional jump diffusion with possibly `infinite-activity'…
Ideal gas dynamics can develop shock-like singularities with discontinuous density. Viscosity typically regularizes such singularities and leads to a shock structure. On the other hand, in 1d, singularities in the Hopf equation can be…
Diffusive transport properties of a quantum Brownian particle moving in a tilted spatially periodic potential and strongly interacting with a thermostat are explored. Apart from the average stationary velocity, we foremost investigate the…
For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.
This paper is concerned with the problem of regularization by noise of systems of reaction-diffusion equations with mass control. It is known that $\textit{strong}$ solutions to such systems of PDEs may blow-up in finite time. Moreover, for…
We discuss recent progress in understanding the dynamical properties of partially hyperbolic diffeomorphisms that preserve volume. The main topics addressed are density of stable ergodicity and stable accessibility, center Lyapunov…
This paper is dedicated to the study of the semilinear fractional diffusion-wave equation. We provide estimates on the families of linear operators related to the problem in the fractional power scale associated with the Laplace operator.…
In the present work, we revisit the so-called regularized short pulse equation (RSPE) and, in particular, explore the traveling wave solutions of this model. We theoretically analyze and numerically evolve two sets of such solutions. First,…
Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key role in mathematical biology and in particular in the study of…
We experimentally and computationally analyze impact-shock-induced stress wave propagation in packings of disordered flexible fibers. We find that dispersive wave propagation, associated with large stress attenuation, occurs much more…
For covering spaces and properly discontinuous actions with compatible diffusion operators, we discuss Lyons-Sullivan discretizations of the associated diffusions and harmonic functions of bounded growth.
The system describing the dynamics of a compressible isentropic fluid exhibiting viscosity and internal capillarity in one space dimension and in Lagrangian coordinates, is considered. It is assumed that the viscosity and the capillarity…
Properties of solutions of generic hyperbolic systems with multiple characteristics with diagonalizable principal part are investigated. Solutions are represented as a Picard series with terms in the form of iterated Fourier integral…
We present the theoretical analysis of the steady state currents and density distributions of particles moving with Langevin dynamics, under the effects of an external potential displaced at constant rate. The Dynamic Density Functional…
The paper studies the interaction of a longitudinal wave with transverse waves in general isotropic and unconstrained hyperelastic materials, including the possibility of dissipation. The dissipative term chosen is similar to the classical…