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A New Graded Algebra Structure on Differential Polynomials: Level Grading and its Application to the Classification of Scalar Evolution Equations in 1+1 Dimension
New Graded Algebra Structure Differential Polynomials Level Grading Classification of Scalar Evolution Equations 1+1 Dimension
2012/4/26
We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$...
Evolution Equations in Functional Derivatives of Many-Particle Systems
BBGKY hierarchy Liouville hierarchy generating functional functional derivative marginal observable
2011/8/25
Abstract: The hierarchies of evolution equations of classical many-particle systems are formulated as evolution equations in functional derivatives. In particular the BBGKY hierarchy for marginal dist...
Convergence to Diffusion Waves for Nonlinear Evolution Equations with Ellipticity and Damping, and with Different End States
evolution equations diffusion waves decay rate energy method a priori estimates
2007/12/11
In this paper, we consider the global existence and the asymptotic behavior of solutions to the Cauchy problem for the following nonlinear evolution equations with ellipticity and dissipative effects:...