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Analytical solution of heat equation with non-homogenous boundary conditions

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#boundary-value-problem #initial-value-problems #parabolic-pde
92
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Uniform boundedness of weak solution

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde #fractional-sobolev-spaces
42
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evolution equation satisfied by projection

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#partial-differential-equations #parabolic-pde #bochner-spaces
158
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Vorticity for the Navier-Stokes equations

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#real-analysis #analysis #partial-differential-equations #fluid-dynamics #parabolic-pde
734
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Is it useful to convert a higher order PDE into a 1st order system?

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#partial-differential-equations #linear-pde #parabolic-pde
153
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In Evans (section on parabolic equations), why can he assume that $u(x_0, t_0)$ is positive?

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#real-analysis #partial-differential-equations #proof-explanation #parabolic-pde
526
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How to show that the mild solution to this parabolic equation is also a classical solution?

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#real-analysis #functional-analysis #partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
450
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A parabolic Morrey-Sobolev inequality

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#sobolev-spaces #parabolic-pde
54
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$u_{xx} + u_x = 0$ ; parabolic PDE

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#partial-differential-equations #parabolic-pde
64
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Pazy's book: Negation of $\overline{\lim}_{x\uparrow a}|f(x)|<\infty$?

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#real-analysis #functional-analysis #partial-differential-equations #parabolic-pde
583
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What does constant along characteristic mean

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#ordinary-differential-equations #partial-differential-equations #linear-pde #parabolic-pde #pseudo-differential-operators
43
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Discrete Fourier Interpolation Proof

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#partial-differential-equations #numerical-methods #fourier-analysis #parabolic-pde
332
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Uniqueness of Non-Linear Heat Equation

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#real-analysis #partial-differential-equations #heat-equation #maximum-principle #parabolic-pde
165
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$ L^p$ regularity for weak solutions of non homogeneous heat equation

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#partial-differential-equations #sobolev-spaces #regularity-theory-of-pdes #parabolic-pde
539
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Motivation for the definition of weak solutions to parabolic equations of second order

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#partial-differential-equations #proof-explanation #parabolic-pde

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