Conservation laws for equations of mixed elliptic-hyperbolic by Lupo D., Payne K.R.

By Lupo D., Payne K.R.

Show description

Read Online or Download Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types PDF

Similar mathematics books

The Mathematics of Paul Erdos II (Algorithms and Combinatorics 14)

This can be the main accomplished survey of the mathematical lifetime of the mythical Paul Erd? s, probably the most flexible and prolific mathematicians of our time. For the 1st time, all of the major components of Erd? s' study are lined in one venture. as a result of overwhelming reaction from the mathematical group, the venture now occupies over 900 pages, prepared into volumes.

Additional info for Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types

Sample text

Friedrichs, Symmetric positive linear differential equations, Comm. Pure Appl. Math. 11 (1958), 338-418. [9] P. ”, Chelsea Publishing Co. New York, 1986. [10] N. Garofalo and E. Lanconelli, Existence and nonexistence results for semilinear equations on the Heisenberg group, Indiana Univ. Math. J. 41 (1992), 71-98. [11] S. Gellerstedt, Sur un probl`eme aux limites pour une ´equation lin´eaire aux d´eriv´ees partielles du second ordre de type mixtes, Dissertation, Uppsala University, Uppsala 1935.

43 [12] V. V. Grushin, Singularities of solutions to certain pseudodifferential and degenerating elliptic equations, Uspehi Mat. Nauk 26 (1971), 221-222. [13] P. Germain and R. Bader, Sur quelques probl`emes relatifs `a l’´equation de type mixte de Tricomi, O. N. E. R. A. Publ. 54 (1952). [14] M. Grillakis, Regularity of the wave equation with a critical nonlinearity, Comm. Pure Appl. Math. 45 (1992), 749-774. [15] S. Hawking and R. Penrose, “The nature of space and time”, The Issac Newton Institute Series of Lectures, Princeton University Press, Princeton, NJ, 1996.

36 of [24]), and so the rest of the proof amounts to a sequence of lengthy calculations which we will briefly summarize. 20) is given by N pr(2) v = v + ϕxj j=1 ∂ ∂ + ϕy + ∂uxj ∂uy N ϕxj xk j,k=1 ∂ ∂uxj xk N ϕxj y + j=1 ∂ ∂ + ϕyy ∂uxj y ∂uyy where the coefficients ϕxj , ϕy , etc. are calculated via a general formula and the expressions uxj , uy , etc. represent the coordinates in the higher order jet spaces. 19) depends only on y, uxj xj , uyy . 21) yields a polynomial in 1, u, Du, D2 u with coefficients that 39 depend on ξ, η, ϕ and their partial derivatives up to order two.

Download PDF sample

Rated 4.10 of 5 – based on 36 votes