相关论文: Partial Differential Equations of Physics
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
In this paper we discuss the first order partial differential equations resolved with any derivatives. At first, we transform the first order partial differential equation resolved with respect to a time derivative into a system of linear…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
A general principle of `causal duality' for physical systems, lying at the base of representation theorems for both compound and evolving systems, is proved; formally it is encoded in a quantaloidal setting. Other particular examples of…
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
Partial differential equations are a convenient way to describe reaction- advection-diffusion processes of signalling models. If only one cell type is present, and tissue dynamics can be neglected, the equations can be solved directly.…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
Partial differential equations are fundamental tools in mathematics,sciences and engineering. This book is mainly an exposition of the various algebraic techniques of solving partial differential equations for exact solutions developed by…
We consider systems of partial differential equations of the form \begin{equation}\nonumber \left\{ \begin{array}{l} u_{xt}=F\left(u,u_x,v,v_x\right),\\ v_{xt}=G\left(u,u_x,v,v_x\right), \end{array} \right. \end{equation} describing…
In this paper we wonder whether a quasilinear system of PDEs of first order admits Hamiltonian formulation with local and nonlocal operators. By using the theory of differential coverings, we find differential-geometric conditions necessary…
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…
The method of characteristics has played a very important role in mathematical physics. Preciously, it was used to solve the initial value problem for partial differential equations of first order. In this paper, we propose a fractional…
In this paper, we introduce a new classical fractional particle model incorporating fractional first derivatives. This model represents a natural extension of the standard classical particle with kinetic energy being quadratic in fractional…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…