engleski

Compactness by compensation and nonlinear parabolic type equation

We investigate conditions under which, for two sequences (ur)(ur) and (vr)(vr) weakly converging to u and v in Lp(Rd ; RN)Lp(Rd ; RN) and Lq(Rd ; RN)Lq(Rd ; RN), respectively, 1/p+1/q≤11/p+1/q≤1, a quadratic form View the MathML sourceq(x ; ur, vr)=∑j, m=1Nqjm(x)ujrvmr converges toward q(x ; u, v)q(x ; u, v) in the sense of distributions. The conditions involve fractional derivatives and variable coefficients, and they represent a generalization of the known compensated compactness theory. The proofs are accomplished using a recently introduced H-distribution concept. We apply the developed techniques to a nonlinear (degenerate) parabolic equation.

compensated compactness

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