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How to reduce the following second order PDE to its canonical form?

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#real-analysis #analysis #partial-differential-equations #linear-pde #parabolic-pde
54
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Finite Element Method and implementation

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#partial-differential-equations #calculus-of-variations #regularity-theory-of-pdes #linear-pde #variational-analysis
641
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How to show instability of downwind and centred scheme

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#partial-differential-equations #hyperbolic-equations #linear-pde
79
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Under which domain transformations are the eigenvalues of $-\Delta$ invariant?

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#functional-analysis #partial-differential-equations #spectral-theory #laplacian #linear-pde
151
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If $U$ is an unitary operator from $L^2(\Omega_1)$ to $L^2(\Omega_2)$, then $U$ commutes with the Laplacian

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#functional-analysis #partial-differential-equations #operator-theory #laplacian #linear-pde
266
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Second order hyperbolic PDE with constant coefficients (analytical solution)

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#partial-differential-equations #linear-pde
136
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Prove the solution to a linear pde is 0 on an open unit ball

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#partial-differential-equations #linear-pde
603
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Eigenvalues and semigroup generated by the Laplacian

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#functional-analysis #operator-theory #spectral-theory #semigroup-of-operators #linear-pde
127
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Fractional powers of an operator associated to a sesquilinear form

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#functional-analysis #operator-theory #spectral-theory #linear-pde #unbounded-operators
329
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Laplacian of the fundamental solution for Laplace's equation

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#partial-differential-equations #laplacian #linear-pde #fundamental-solution
98
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Isometric domains are isospectral for the Laplacian

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#functional-analysis #spectral-theory #laplacian #semigroup-of-operators #linear-pde
175
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Characteristics of semilinear PDE $xu_x+yu_y+xyu_z=0$

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#partial-differential-equations #characteristics #linear-pde
57
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Existence for $-\Delta u + u + f(u) =0$ when $f$ is a compact operator?

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#functional-analysis #elliptic-equations #linear-pde
833
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Poisson equation, exact solution

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#partial-differential-equations #linear-pde
1.9k
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Intuition behind the maximum principle for the heat equation

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#partial-differential-equations #heat-equation #linear-pde #parabolic-pde

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