相关论文: A Conservation law for a sedimentary basin submitt…
We establish the equations which translate a conservation law for the problem of the seismic response of an above-ground structure (e.g., building, hill or mountain) of arbitrary shape and inquire whether both the implicit (formal) and…
The problem, of 2D canonical nature, examined herein in the space-frequency framework, concerns a SH-polarized plane body seismic wave propagating in a hard, non lossy half space (bedrock) containing a soft, lossy cylindrical basin of…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
The hydrodynamic response of the inviscid small shearing box model of a midplane section of a rotationally supported astrophysical disk is examined. An energy functional ${\cal E}$ is formulated for the general nonlinear problem. It is…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
The paper is concerned with a scalar conservation law with discontinuous gradient-dependent flux. Namely, the flux is described by two different functions $f(u)$ or $g(u)$, when the gradient $u_x$ of the solution is positive or negative,…
An overlooked conservation law for near-inertial waves propagating in a steady background flow provides a new perspective on the concentration of these waves in regions of anticyclonic vorticity. The conservation law implies that this…
A complete classification of all low-order conservation laws is carried out for a system of coupled semilinear wave equations which is a natural two-component generalization of the nonlinear Klein-Gordon equation. The conserved quantities…
The letter considers non-isothermal fluid flows and revises simplifications of basic hydrodynamic equations for such flows arriving eventually to a generalization of the Oberbeck-Boussinesq approximation valid for arbitrary equation of…
We derive an energy conservation law for the system of gravitational perturbations on the Schwarzschild spacetime expressed in a double null gauge. The resulting identity involves only first derivatives of the metric perturbation.…
We construct Lie point symmetries, a closed-form solution and conservation laws using a non-Noetherian approach for a specific case of the Gorini-Kossakowski-Sudarshan-Lindblad equation that has been recast for the study of non-relativistic…
The conditions of existence of extra mass flux in single component dissipative non-relativistic fluids are clarified. By considering Galilean invariance we show that if total mass flux is equal to total momentum density, then mass,…
The appearance of a geometric flow in the conservation law of particle number in classical particle diffusion and in the conservation law of probability in quantum mechanics is discussed in the geometrical environment of a two-dimensional…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
Conservation laws are computed for various nonlinear partial differential equations that arise in elasticity and acoustics. Using a scaling homogeneity approach, conservation laws are established for two models describing shear wave…
Symmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible medium. This nonlinear wave equation is widely…
In the work it has been shown that there are two types of the conservation laws. 1. The conservation laws that can be called exact ones. They point to an avalability of some conservative quantities or objects. Such objects are the physical…
Classifications of symmetries and conservation laws are presented for a variety of physically and analytically interesting wave equations with power onlinearities in n spatial dimensions: a radial hyperbolic equation, a radial Schrodinger…
A simple conservation law formula for field equations with a scaling symmetry is presented. The formula uses adjoint-symmetries of the given field equation and directly generates all local conservation laws for any conserved quantities…
We consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the "flux" is defined as a flux field of n-forms depending on a parameter (the unknown…