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Deduce positivity of solution of linear parabolic PDE from non-negative initial data

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#maximum-principle #linear-pde
227
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Schrödinger Operator (spectrum)

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#spectral-theory #linear-pde
506
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Linear first order PDE $u_x+u_t=u$ with the method of characteristics

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#partial-differential-equations #characteristics #linear-pde
215
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Some questions about separation of variables and convergence in Laplace's equation

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#partial-differential-equations #harmonic-functions #laplacian #pointwise-convergence #linear-pde
67
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$l^{p}$ and $L^{p}$ applications in PDEs

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#functional-analysis #analysis #partial-differential-equations #lp-spaces #linear-pde
78
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Are these two PDEs equivalent somehow?

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#partial-differential-equations #wave-equation #linear-pde
85
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1D wave equation - solving a specific initial/boundary value problem

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#partial-differential-equations #boundary-value-problem #wave-equation #initial-value-problems #linear-pde
43
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Solving a linear non-separable first order PDE

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#partial-differential-equations #linear-pde
82
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References regularity of solutions to linear system of first order PDE

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#partial-differential-equations #reference-request #regularity-theory-of-pdes #linear-pde #parabolic-pde
223
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Intuition for Green's function for the Heat Equation

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#partial-differential-equations #heat-equation #greens-function #linear-pde #fundamental-solution
190
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Cosh and Sinh in the Wave equation.

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#partial-differential-equations #fourier-series #wave-equation #linear-pde
194
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Solution of Poisson equation for $f(x,y)=1$

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#partial-differential-equations #elliptic-equations #linear-pde #poissons-equation
76
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Is there a name for this differential equation?

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#partial-differential-equations #linear-pde
33
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How does one see currents as solutions to continuity equations?

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#partial-differential-equations #reference-request #linear-pde
30
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Solve a coupled PDE in a rectangle

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#regularity-theory-of-pdes #linear-pde

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