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I am reading the proof of the properties of Bogovskii operator in the book Introduction to the Mathematical Theory of Compressible Flow. Let $B^\epsilon(y) = \{ x : |x-y| > \epsilon \}$, $f$ and $... 1answer 203 views ### An answer to this system of PDE's Planning of the question: Let$(M,g)$be a Riemannian manifold and$TM$be its tangent bundle The isotropic almost complex structures$J_{\delta , \sigma}$were introduced by Aguilar on the ... 1answer 42 views ### Approximate largest eigenvalue of Monodromy matrix Does anyone know the procedure (or have pseudo code) to approximating the largest eigenvalue of a monodromy matrix? Or even to approximate the monodromy matrix itself? There is no explicit solution ... 0answers 49 views ### Show this function is strictly concave Please help me show that$f(w)$is strictly concave in$w\in[0,\infty)$:$f(w)=\sum_{j=1}^N P_j (w)\cdot u_j $where$P_j (w)=\sqrt{w}\int _{-\infty}^{\infty}\Pi_{k\neq j}\{\Phi[\sqrt{w}(v-u_k)]\}...
Suppose I have the following PDE: $\frac{\partial y}{\partial t} = \frac{\partial}{\partial x}\left[(1-y)^3y^3\left(\sin \theta + \frac{\partial y}{\partial x}\cos \theta\right) \right]$ I notice ...