New monotonicity formulae for semi-linear elliptic and parabolic systems

O ct 2 00 5 NEW MONOTONICITY FORMULAE FOR SEMI - LINEAR ELLIPTIC AND PARABOLIC SYSTEMS

where t1 < t2 are two constants, (fi(~u)) is given as above. Our new monotonicity formulae are focused on more attention to the monotonicity of non-linear terms. Our point of view is that we introduce an index called β to measure the monotonicity of the non-linear terms in the problems. The index in the study of monotonicity formulae is very useful in understanding the behavior of blow up seque...

Quasi-linear Parabolic Systems in Divergence Form with Weak Monotonicity

We consider the initial and boundary value problem for the quasi-linear parabolic system ∂u ∂t − div σ (x, t, u(x, t),Du(x, t)) = f on × (0, T ), u(x, t) = 0 on ∂ × (0, T ), u(x, 0) = u0(x) on for a function u : × [0, T ) → R with T > 0. Here, f ∈ Lp(0, T ;W−1,p ( ;Rm)) for some p ∈ (2n/(n + 2),∞), and u0 ∈ L2( ;Rm). We prove existence of a weak solution under classical regularity, growth, and ...

a new type-ii fuzzy logic based controller for non-linear dynamical systems with application to 3-psp parallel robot

abstract type-ii fuzzy logic has shown its superiority over traditional fuzzy logic when dealing with uncertainty. type-ii fuzzy logic controllers are however newer and more promising approaches that have been recently applied to various fields due to their significant contribution especially when the noise (as an important instance of uncertainty) emerges. during the design of type- i fuz...

Symmetry and Monotonicity Properties for Positive Solutions of Semi-linear Elliptic Pde's

New Formulae for Efficient Elliptic Curve Arithmetic

This paper is on efficient implementation techniques of Elliptic Curve Cryptography. In particular, we improve timings for Jacobiquartic (3M+4S) and Hessian (7M+1S or 3M+6S) doubling operations. We provide a faster mixed-addition (7M+3S+1d) on modified Jacobiquartic coordinates. We introduce tripling formulae for Jacobi-quartic (4M+11S+2d), Jacobi-intersection (4M+10S+5d or 7M+7S+3d), Edwards (...