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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 $C^{\infty}$...
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:...