ABSTRACT
Integrates two fields generally held to be incompatible, if not downright antithetical, in 16 lectures from a February 1990 workshop at the Argonne National Laboratory, Illinois. The topics, of interest to industrial and applied mathematicians, analysts, and computer scientists, include singular per
TABLE OF CONTENTS
chapter |16 pages
References
of contrasting spatial of Internal Layers and Diffusive Interfaces, SIAM, Philadelphia,
chapter |3 pages
Measurement of for Different Values of c
lo [0(x, h(r)dr lo 8y 8rk rx !!_0(x -r,y) fo(r)dr. lo 8y 8rk lo By[0(x,
chapter |12 pages
of Residual
S(t))/E t S1t)jE to)/f f locally linear S1t)jE to)/f3f4 lxf(u) lx ( G (!, u, D..t,D..x) u(x, tk) given.
chapter |8 pages
It does not, however, hold for the Navier-
In C is positive definite. Then there exists 8 of (5) are real when s is real and s > 8. iv and, by an integration by parts, obtain sIn Mv vHTv B(v,A)= vHDoov)+vHcv)
chapter |6 pages
References
of the ex- tinction limit of curved flames, Combust. Sci. and Tech. 64 (1989), 187-198. of solu- tions of semilinear elliptic equations, preprint. of solutions of semilinear
chapter |2 pages
< < are converging to a steady-state
of the limit cycle of the van der Pol equation, SIAM J. Appl. Math. 42 (1982),
chapter 5|2 pages
Reduced Equations
dtu+ aV'P+ F P1Y' · u a is the specific volume, P is the pressure, and 1 is the ratio of specific u · V' is the total time
chapter |5 pages
K; and the activation energy, E. The initial conditions
=Yo, u -Ao. t) = u(Lo, t) = 0.
chapter |13 pages
References
interaction of edge rarefactions with finite reaction zones, J. Fluid Mechanics 171 of two-dimensional detonation with detona- tion shock dynamics,
chapter |5 pages
= -oo,
t) Oo[Vb]wo(p, v, t)dp. I/:). Vb(p, TJ)}( t) exp( iTJv)dTJdp t) denotes the Fourier transform of the function f( v, t) in (28) in the v direction. p -TJ and 0 I v,
chapter |2 pages
Finite Difference Methods
u:n.+l vfit [(D(Ul+ (Ul+t,j- UlJ) (D(UT".) [(D(UlJ+ D(U[j)) (U;j+ UlJ) (D(U;j) D(U;j_ (U;j-
chapter |12 pages
< t < T where the solution of (1)-
T the maximal number such that the solution exists for 0 u(x, t)--+ oo if t--+ T. tn to t T) such that (xm, tm)· Such points (x T) are called blow-up points. (x) has at most two local maxima, see [14, 8]). f 4) that C > 0,
chapter |5 pages
It follows that < 0, >
0(8) and R(x) R(O) 0(8) uv(x),Rv(x) with an +0(e -ixifv), Rv R+O( e-ixifv) R(x) p'(x, t), u U(x) u'(x, t), _xs=O.
chapter |1 pages
R)¢dx
2RU)¢1x=xa jxa ax (U 2RU)¢dx v¢2xlx=xa· (U, R)¢1x=xo = 0((1>.1 8)v), and to first approximation we have (U, R)¢1x=xo J', 2RU)¢1x=xo -lxo
chapter |2 pages
of solutions of Burgers'
equation, Appl. Num. Math. 2 (1986), 161-179. Equation, Academic Press, New York, 1989.
chapter |4 pages
iff( u)
f( u) uP+u, showed that the solution p is supercritical). In fact, for balls of certain sizes they were able to show that at least
chapter |2 pages
> 0 and f is superlinear, i.e., f(u)fu is monotone increasing. The goal is to
J, such that there is at most one positive solution of the differential 8uf 8a satisfies the [q(r)f'(u)]w w'(O)
