Mystery surrounds how a rare 12-metre (40ft) fin whale came to be washed up on a beach in Norfolk.
Let (alpha in (0,1), fin C^{infty }(Q)) and w be a smooth solution of (L_{epsilon, A}w=f) on Q.
Let (alpha in (0,1), fin C^{infty }(Q)) and w be a smooth solution of (L_{epsilon, A^epsilon }w=f) on Q.
In order to establish the results, we assume that the following conditions are satisfied: ((A_{1})) (fin C 0,1 times 0,+infty),[0,+infty))). ((A_{2})) (qin C 0,1),+inftyfty))), and q does not vanish identically on any subinterval of ((0,1)).
For (0leq r<1), (fin H mathbb{D})), we set begin{aligned}& M_{p}(f,r)= biggl(frac{1}{2pi}int_{0}^{2pi} biglvert fbigl(re^{itheta}bigr) bigrvert ^{p}, { mathrm{d}}theta biggr)^{1/p},quad 0 < p < infty, & M_{infty}(f,r)=max_{0leqtheta leq2pi}biglvert f bigl(re^{itheta}bigr bigrvert.
To state our results, we make the following assumptions: ((textbf{A}_{textbf{1}})) : (fin C overline{Omega} timesmathbb{R}^,mathbb{R})), (f x,0 equiv0), and lim_{trightarrow 0^frac{f x,t)}{t^{p-1}}=+infty, quadquad lim _{trightarrow infty}frac{f x,t)}{t^{p^{ast}(s -1}}=0 quadtext{uniformly for } xinoverline{ Omega}.
When (M s)equiv1), (p(t)equiv2), condition (H1) and (H2) were introduced in [2], which is an extension of the usual sublinear growth condition, i.e. there exist (alphain[0,1)), (fin L^{1}(0,T;mandbb{R}^)) and (gin L^{1}(0,T;mathbb{R}^)), such that biglvert nabla F_{1} t,x bigrvert leq f(t)vert xvert ^{alpha}+g(t) for all (xinmathbb{R}^{N}) and a.e. (tin[0,T]).
(F V,t)=V^{n}f(t)), (Vinmathbb{R}), (t>0), with (n<1), (fin L^{1}_{mathrm{loc}}(mathbb{R}^)), (f>0) and (lambda, delta, eta>0), Then the function v defined by v x,t)=widetilde{X}(x widetilde{T}(t),quad xgeq0, tgeq0 (116) is a solution with separated variables to Problem P̃, where T̃ is the solution of the initial value problem (15 - 16).
There could be 20,000 fin whales off Iceland's coast, or only 3,000".
3BR, 2.5BA TH, 10 mins south of Baltimore, just off I-95, fin'd bsmt, fp, bar.
