As well, (8.3) holds for any (fin L^{infty}_{mu}).
Then, for any (fin L^{m}(Omega)) with (1leq mleq1+ frac{1}{problemoblem (1.1) has a weak solution.
The limit relation (8.2) holds for any (fin L^{p}_{mu}) ((1le p
For any (fin mathscr {S}^{prime}(G)), we set (Delta_{j} f=f*varphi_{j}).
Baseline comparisons are done with a heat sink filled with PCM, without any fin.
Then the sequence ({L_{n,alpha}(f;x)}) converges to f uniformly on ([0,1]) for any (fin C[0,1]).
It has been found that: (1) increasing fin length increases NuH and ε; (2) increasing Ra increasesNuH for any fin-array geometries and (3) for any fin-array geometry and at Ra > 10,000, increasing Ra decreases ε while for fin-array geometries of large fin spacing and at Ra < 10,000, increasing Ra increases ε.
For any (fin L^{varphi}), we only need to prove, for any (Bin mathcal{B}), mathrm{I}:=frac{1}{vert Bvert } int_{B} biglvert f(x bigrvert,dx< infty.
For any (fin L^{infty}(Bbb {R}^{n})), the equation lim_{krightarrowinfty}M^{k}f(x)=|f|_{infty} (4.2) holds for any (xin Bbb {R}^{n}).
If (C_{T}neqemptyset), then the following statements hold: (1) For any (fin C_{T}), (T|_{[f]_{widetilde{G}}}) has a fixed point.
Then for any (fin C_{rho}^{k}(mathbb{R}^)), we have lim_{nrightarrowinfty}biglVert D_{n,q}(f;x -f(x -fgrVert _{rho }=0.
