From c8b5fefa146d4254103516d62848c422cc277ae4 Mon Sep 17 00:00:00 2001 From: flavis Date: Tue, 30 Jun 2020 19:26:30 +0200 Subject: [PATCH] add one more graphic to ana17 --- ana17.tex | 37 +++++++++++++++++++++++++++++++++++++ analysisII.pdf | Bin 843404 -> 847625 bytes 2 files changed, 37 insertions(+) diff --git a/ana17.tex b/ana17.tex index 30f29a8..43bc572 100644 --- a/ana17.tex +++ b/ana17.tex @@ -58,6 +58,42 @@ \text{Graph}(y) = \{ (t, y(t)) , t \in I_{\text{max}}\} \] unbeschränkt ist, weil $t \to t_0 + T^{*} = \infty$ oder $\Vert y(t) \Vert \xrightarrow{t \to t_0 + T^{*}} \infty$. + + \begin{figure}[h] + \centering + \begin{tikzpicture}[declare function={f(\x) = tan(deg(\x-2));}] + \begin{axis}% + [default 2d plot, + grid=none, + ymax=4, + ymin=-4, + xmin=0, + xmax=4, + xtick=\empty, ytick=\empty, + ] + \addplot[domain=0.56:3.56,samples=100,smooth,red] {f(x)}; + \draw[dashed] (0.56, 5) -- (0.56, -5); + \draw[dashed] (3.45, 5) -- (3.45, -5); + \draw (2.56, {f(2.56)}) node[fill,inner sep=1pt]{}; + \draw (2.56, {f(2.56)}) node[draw,shape=rectangle,minimum width=10mm, minimum height=7mm, + anchor=center] {}; + \draw (2.85, {f(2.85)}) node[fill,inner sep=1pt]{}; + \draw (2.85, {f(2.85)}) node[draw,shape=rectangle,minimum width=9mm, minimum height=7mm, + anchor=center] {}; + \draw (3.02, {f(3.02)}) node[fill,inner sep=1pt]{}; + \draw (3.02, {f(3.02)}) node[draw,shape=rectangle,minimum width=6mm, minimum height=6mm, + anchor=center] {}; + \draw (3.12, {f(3.12)}) node[fill,inner sep=1pt]{}; + \draw (3.12, {f(3.12)}) node[draw,shape=rectangle,minimum width=5mm, minimum height=5mm, + anchor=center] {}; + \draw (3.18, {f(3.18)}) node[fill,inner sep=1pt]{}; + \draw (3.18, {f(3.18)}) node[draw,shape=rectangle,minimum width=4mm, minimum height=4mm, + anchor=center] {}; + \draw (3.65, -4) node{$\partial D$}; + \end{axis} + \end{tikzpicture} + \caption{Schrittweise Fortsetzung einer Lösung bis zum Rand von $D$} + \end{figure} \end{bem} \begin{korollar}[Globale Existenz] @@ -227,6 +263,7 @@ \end{tikzpicture} \caption{Für $y_0 = 0$ existieren beliebig viele zusammengesetzte Lösungen.} \end{subfigure} + \caption{Zur Uneindeutigkeit von AWA} \end{figure} Beobachtung: $f(t,x)$ ist stetig auf $\R \times \R$, aber $f(t,x)$ ist nicht Lipschitz stetig diff --git a/analysisII.pdf b/analysisII.pdf index 814834cc43007d5f62ed0f24b982572aa80c79fc..08eba110f64e6c3ec8afab7a97aa51bc9ce56e95 100644 GIT binary patch delta 78091 zcmXt-18lC%)5dGtwr%6ow(V2fd}`Z0wQbuzZBK36w*Gy;_rFW~8!C0*3a4qsU+y?T7U z9&p#QbqUh1idZ)Xg9P~mU+w~8^e(NP%Dulz8Y!MR))+?T(hfR~YdfzID!JdjUUPeV z;sF;s|=cO#p0C)Pw@>Gv+hb-|xQU0$tyi3AAC1T{3`= zx7)(nFOTo?uidReNW_;_g01hjF#-XA%k%Bv=<{tKz~>VQt*UFs{p(k=Q?s{IO|&2YEGyud=h5pWESXM~kz5hiahDhR~V`19jS*Tkp%U0q}92 zc_l?jcZV!FfteP<{dJ{#;#^Kn_xk6a6`Q5a=W710328l^S%-woXv*J> zU>J^ep>?zW=X>qbWRU0iym{CK=G-@yjQL#L*1J$~O^u!P&XfuBl)DpfXLue)N5t%p zUw|Y`y!JWiW?a0h9l_o2-0>m=1lATAb}}haH3im_fjZ~bYhI8H0iVNX7k-=hgnMkI z=t_T4R8B>(2mpSxP z4JA7Va*L=z$}4c%8WIWnPKKx z$48ED1UVZ+X^jj3#+?p1eu@1JoldqZTI^tCdn+qfCppMlpzh8a?3D3 zm>=>>p2)ZgM>3H2cfM-j5tw#_Pz&-dBEfq2Kg=h>5U^5OVVda)0;2j8(^_OcHA-P2 zKAK?@@D~N4Cm?7LRM@D1Clc?mZg(Y6n6g>iRfq*tI%BP1z<_Q;9keLXIlV3#Ssg}T zJjh<=81zD-sg@{B@DPLXD;gYSr71KoD0KZCByqn%Rm~so7gH4D*d_`^7`zp)lC|g? zpdC}zft+|@X*ubeG^7Gdt0xizx?-3h;AuGJU;r91v6kv0d{+%qNqnTFKU2Uz z9H$aQ(#VWt0Q(9A7)QRxO137TfjrO# zNNJGCW3Zq^9Jb^H6RmQ=5LBq>JRH`La?%BG{uVGY(LtD%2?`7dVgaor)XXq6G_hh3 z<6ZInj{t}*P4@9H4YC-CanbA4LXhGd{x2!2;zR?0)JlY@b`nvt;IU-OYN-5hu^Y1Z z0>%dLAuZgjbkH)SEGm*&SVPr_UAZPPRx06NY>E6#N))xqAV+XoEx?1n!uu)|)o-LD zqPtfgrbF{c`(r0C7c`BRj(6Tyz)^DPQ+1iJnI-~J3X|~ryfPNJ=cGAeg=L`vdnOfA zt6lT~@i(Z`P$+v`oc{l6xS74%O3gTc;4NVR;N{_9QjyTm0T~$5CNx0Qq;8(ru)}I< zpfo_Do<%wyI%<7k_&5_RDum-a#IMFxSYTy~gW8h8&`$8-tGsV^M4~{~WC4zLz*_z3 z1+kH2aVwW07O;g=dNYG)fwSu@Pl>S(b2;h?~9)6eHsNb~vgs z98<_KK>@23Nc5$_;E^U1Bw&~qgoqcU>N9GDFi51u`BR-FW17C*l01VUUQl zKqTBpYg^LLpK0rkP;+#ngLq+G)z(`Ss^Qeb{TC>=L3BJ(kY

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