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$L^\infty(L^\infty)$-boundedness of DG($p$)-solutions for nonlinear conservation laws with boundary conditions
nonlinear conservation laws boundary conditions
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2010/11/18
We prove the $L^\infty(L^\infty)$-boundedness of a higher-order shock-capturing streamline-diffusion DG-method based on polynomials of degree $p\geq 0$ for general scalar conservation laws. The estim...
On the spectral vanishing viscosity method for periodic fractional conservation laws
spectral vanishing viscosity method periodic fractional conservation laws
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2010/11/22
We introduce and analyze a spectral vanishing viscosity approximation of periodic fractional conservation laws. The fractional part of these equations can be a fractional Laplacian or other non-local ...
On a kind of Noether symmetries and conservation laws in k-cosymplectic field theory
Symmetries Conservation laws Noether theorem Hamiltonian field theories
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2010/12/6
This paper is devoted to studying symmetries of certain kinds of k-cosymplectic Hamiltonian
systems in first-order classical field theories. Thus, we introduce a particular class of
symmetries and s...
Factorization systems induced by weak distributive laws
Factorization systems weak distributive laws
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2010/11/29
We relate weak distributive laws in SetMat to strictly associative (but not strictly unital) pseudoalgebras of the 2-monad (−)2 on Cat. The corresponding orthogonal factorization systems are cha...
Selfdecomposable Laws Associated with Hyperbolic Functins
Hyperbolic characteristic functions class L or SD probability distribution
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2010/12/8
t is shown that the hyperbolic functions can be associated with selfdecomposable distributions (in short: SD probability distributions or L´evy class L probability laws). Consequently, they admi...
A weak mixed distributive law (also called weak entwining structure [6]) in a 2-category consists of a monad and a comonad, together with a 2-cell relating them in a way which generalizes a mixed dist...
We derive the representative Bernstein measure of the density of (X )− /(1− ), 0 < < 1, where X is a positive stable random variable, as a Fox-H function. Our result makes more explicit...
Conservation laws for under determined systems of differential equations
Adjoint equation nonlinear differential equation variational problem Lagrangian
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2010/12/8
This work extends the Ibragimov’s conservation theorem for partial differential equations
[J. Math. Anal. Appl. 333 (2007 311-328] to under determined systems of differential equations.
The concepts...
The effect of reported high-velocity small raindrops on inferred drop size distributions and derived power laws
reported high-velocity small raindrops inferred drop size distributions derived power laws
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2010/8/16
It has recently been shown that at high rainfall intensities, small raindrops may fall with much larger velocities than would be expected from their diameters. These were argued to be fragments of rec...
Conservation laws and normal forms of evolution equations
Conservation laws normal forms evolution equations
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2010/4/6
We study local conservation laws for evolution equations in two independent variables. In particular, we present normal forms for the equations admitting one or two low-order conservation laws. Exampl...
Classical Scaling Symmetry Implies Useful Nonconservation Laws
Nonconservation Laws symmetry dynamically
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2010/4/2
Scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action and do not lead to conservation laws. Nevertheless, by an extension of Noether's theorem, scal...
Conservation laws for strings in the Abelian Sandpile Model
Conservation laws Abelian Sandpile Model
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2010/4/2
The Abelian Sandpile generates complex and beautiful patterns and seems to display allometry. On the plane, beyond patches, patterns periodic in both dimensions, we remark the presence of structures p...
Notes Concerning "On the Origin of Gravity and the Laws of Newton" by E. Verlinde
structure of spacetime partition function phase transition
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2010/3/18
We point out that certain equations which, in a very recent paper written by E. Verlinde, are postulated as a starting point for a thermodynamical derivation of classical gravity, are actually consequ...
Noether Symmetries and Covariant Conservation Laws in Classical, Relativistic and Quantum Physics
Noether Symmetries Quantum Physics Covariant Conservation Laws
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2010/3/18
We review the Lagrangian formulation of Noether symmetries (as well as "generalized Noether symmetries") in the framework of Calculus of Variations in Jet Bundles, with a special attention to so-calle...
Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method
conservation laws quad-graph equations
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2010/4/1
The application of the Gardner method for generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner meth...