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What's wrong with the following PDE

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Are the following PDEs equivalent?

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266
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#boundary-value-problem #heat-equation #regularity-theory-of-pdes #singularity #parabolic-pde
171
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Heat equation and smoothness effect

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#partial-differential-equations #regularity-theory-of-pdes #parabolic-pde
166
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How can I solve these second order PDE's?

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#partial-differential-equations #fourier-transform #nonlinear-system #parabolic-pde
830
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#reference-request #partial-differential-equations #parabolic-pde
196
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#partial-differential-equations #linear-pde #parabolic-pde
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Heat equation $u_t=u_{xx},u_x(t,0)=0,u(0,x)=e^{-x^2}$

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#partial-differential-equations #fourier-series #heat-equation #linear-pde #parabolic-pde
946
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$N$-dimensional Heat equation + BC's

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#partial-differential-equations #heat-equation #parabolic-pde #fundamental-solution
230
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Proposition $2.1$ - Lectures on Mean Curvature Flow by Xi-Ping Zhu

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#proof-explanation #parabolic-pde #mean-curvature-flows
157
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Finding stationary distribution of a 2D stochastic process

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#stochastic-processes #stochastic-differential-equations #parabolic-pde
245
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Estimates of fundamental solution of heat equation in Sobolev space

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#real-analysis #partial-differential-equations #heat-equation #regularity-theory-of-pdes #parabolic-pde
220
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#partial-differential-equations #parabolic-pde
158
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Eigenfunctions of Parabolic Differential Operator`

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#partial-differential-equations #numerical-methods #parabolic-pde
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Solving parabolic partial differential equations with polynomial coefficients

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