Related papers: Beyond partial differential equations: A course on…
We consider the small time semi-classical limit for nonlinear Schrodinger equations with defocusing, smooth, nonlinearity. For a super-cubic nonlinearity, the limiting system is not directly hyperbolic, due to the presence of vacuum. To…
We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
In this paper we use key elements of the Olver's approach to Hamiltonian evolution equations in partial derivatives and propose an algebraic construction appropriate for Hamiltonian evolution systems with constraints.
The paper concerns the theory of parabolic equations on a broad class of closed subsets of Euclidean space possessing a kind of tangent structure. A necessary framework for considering evolutionary problems is developed, and fundamental…
We present an investigation of vibrational features in water clusters performed by means of our recently established divide-and-conquer semiclassical approach [M. Ceotto, G. Di Liberto, and R. Conte, Phys. Rev. Lett. 119, 010401 (2017)].…
Some higher-order quasilinear parabolic, hyperbolic, and nonlinear dispersion equations are shown to admit various blow-up, extinction, and travelling wave solutions, which reduce to variational problems admitting countable families of…
We consider multi-gradient fluids endowed with a volumetric internal energy which is a function of mass density, volumetric entropy and their successive gradients. We obtained the thermodynamic forms of equation of motions and equation of…
New technique of integration of certain types of partial differential equations is developed. For this purpose non-commutative integration over Cayley-Dickson algebras is used. Applications to non-linear vector partial differential…
In this paper we study a semilinear hyperbolic-parabolic system as a model for some chemotaxis phenomena evolving on networks; we consider transmission conditions at the inner nodes which preserve the fluxes and non- homogeneous boundary…
We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the…
This paper is concerned with supersolutions to parabolic equations of the form \begin{equation} \partial_t U (x,t)-D(x)\Delta U(x,t)=0, \quad (x,t)\in \mathbb{R}^N \times (0,\infty), \end{equation} where $D\in C(\mathbb{R}^N)$ is positive.…
We present a comprehensive theory of critical spaces for the broad class of quasilinear parabolic evolution equations. The approach is based on maximal $L_p$-regularity in time-weighted function spaces. It is shown that our notion of…
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded…
Following a recently introduced approach to approximate Lie symmetries of differential equations which is consistent with the principles of perturbative analysis of differential equations containing small terms, we analyze the case of…
We search for non-trivial relativistic solutions of the hydrodynamic equations with quasi-inertial flows such as in the Bjorken-like models. The problem is analyzed in general and the known results are reproduced by a method proposed. A new…
We give solutions to several decision problems in word hyperbolic groups
To obtain new types of exact travelling wave solutions to nonlinear partial differential equations, a number of approximate methods are known in the literature. In this study, we extend the class of auxiliary equations of Fibonnacci&Lucas…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
We aim to study nonnegative, global solutions to a general class of nonlocal parabolic equations with bounded measurable coefficients. First, we prove a Widder-type theorem. Such a result has previously been studied only for certain…