Decay and growth for a nonlinear parabolic difference equation

Decay and Growth for a Nonlinear Parabolic Difference Equation

We prove a difference equation analogue of the decay-of-mass result for the nonlinear parabolic equation ut = ∆u+ μ|∇u| when μ < 0, and a new growth result when μ > 0.

A Nonlinear Differential-difference Equation of Growth.

A Nonlinear Parabolic - Sobolev Equation

Let M and I, be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and j(Mx My) i~(Lx Ly)( > / Mx My / for all 01 > 0 and pairs s, y in D(M) n D(L). Then there is a unique solution of the Cauchy problem (Mu(t))’ + Lu(t) = 0, Mu(O) = v0 . When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of ge...

BEHAVIOR OF SOLUTIONS TO A FUZZY NONLINEAR DIFFERENCE EQUATION

In this paper, we study the existence, asymptotic behavior of the positive solutions of a fuzzy nonlinear difference equation$$ x_{n+1}=frac{Ax_n+x_{n-1}}{B+x_{n-1}}, n=0,1,cdots,$$ where $(x_n)$ is a sequence of positive fuzzy number, $A, B$ are positive fuzzy numbers and the initial conditions $x_{-1}, x_0$ are positive fuzzy numbers.

Decay of Mass for a Semilinear Parabolic Equation

We study the decay of I (t) = R u(:; t) where u is a nonnegative solution to u t ? u + jruj q = 0 in R n R + with n 1. If 1 q n+2 n+1 then I (t) ! 0 if I (0) < 1 and inf t>0 I (t) > 0 if q > n+2 n+1 .