相关论文: Conservation Laws of Variable Coefficient Diffusio…
Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently…
In this paper we consider a system of equations that describes a class of mass-conserving aggregation phenomena, including gravitational collapse and bacterial chemotaxis. In spatial dimensions strictly larger than two, and under the…
This short survey paper is concerned with a new method to prove global well-posedness results for dispersive equations below energy spaces, namely $H^{1}$ for the Schr\"odinger equation and $L^{2}$ for the KdV equation. The main ingredient…
In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for investigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive symmetries…
Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which…
We continue the investigation of the correspondence between systems of conservation laws and congruences of lines in projective space. Relationship between "additional" conservation laws and hypersurfaces conjugate to a congruence is…
The connection between symmetries and conservation laws as made by Noether's theorem is extended to the context of causal variational principles and causal fermion systems. Different notions of continuous symmetries are introduced. It is…
In this paper, we investigate the conservation laws of different type of particles in theories with a universal gravity/matter coupling. The result brings new insights about previous studies on universal gravity/matter theories. Especially,…
We show for a variety of classes of conservative PDEs that discrete gradient methods designed to have a conserved quantity (here called energy) also have a time-discrete conservation law. The discrete conservation law has the same conserved…
We use the Lagrange-Noether methods to derive the conservation laws for models in which matter interacts nonminimally with the gravitational field. The nonminimal coupling function can depend arbitrarily on the gravitational field strength.…
We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…
A diffusive lattice gas is characterized by the diffusion coefficient depending only on the density. The Green-Kubo formula for diffusivity can be represented as a variational formula, but even when the equilibrium properties of a lattice…
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that preserve the important mass conservation locally on each…
A common feature of systems of conservation laws of continuum physics is that they are endowed with natural companion laws which are in such case most often related to the second law of thermodynamics. This observation easily generalizes to…
We discuss the role of the conservation laws related with U(1) internal symmetry group in the statistical model description of particle productions in ultrarelativistic heavy ion collisions. We derive and show the differences in particle…
We formulate a family of scalar softening laws by setting the stored-energy density $\psi(\eta)=\int_{0}^{\eta}[1-F(s)]d s$, where $F$ ranges over exponential, Cauchy, logistic, half-normal, Gudermannian, hypergeometric, radical, rational,…
We explain the necessity of application of semi-metric in general relativity. A detailed discussion on the energy-momentum conservation in the general relativity is presented using the mathematical tool of semi-metric. By means of the…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and…
For the Euler equations governing compressible isentropic fluid flow with a barotropic equation of state (where pressure is a function only of the density), local conservation laws in $n>1$ spatial dimensions are fully classified in two…