List questions from partial-differential-equations

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Constructing a specific normalised test function.

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Fourier transform help for solving $u_t+u_{xxxx}+u_{xx}=0$

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Compatibility of initial and boundary conditions

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Show that $L[v^2] := \Delta(v^2) + \frac{2}{w} \sum_{i=1}^n w_{x_i} (v^2)_{x_i} \ge 0$

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Non-examples for the Kato-Rellich Theorem

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Pair of PDEs to be solved together

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123

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Intuitive interpretation of $\frac{\partial S(a,t)}{\partial t} = -\frac{\partial S(a,t)}{\partial a}$

Published on 13 Apr 2026 - 19:11

87

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Local Mollification of a $L^1$ function

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37

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Solutions of a PDE in two dimensions

Published on 09 Apr 2026 - 13:42

147

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References on estimating capacities (Newton, Martin etc) for sets & alternative formulations.

Published on 11 May 2026 - 1:48

324

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Solving PDE via Fourier Transform & Uniqueness

Published on 13 Apr 2026 - 2:59

List Question

Evans PDE(2nd edition) Problem 5.11: If $Du=0$ a.e. , does $u=c$ a.e.?

Constructing a specific normalised test function.

Fourier transform help for solving $u_t+u_{xxxx}+u_{xx}=0$

Compatibility of initial and boundary conditions

Show that $L[v^2] := \Delta(v^2) + \frac{2}{w} \sum_{i=1}^n w_{x_i} (v^2)_{x_i} \ge 0$

normalized mean curvature flow with convex initial hypersurface has finite velocity

Elliptic partial differential equations and elliptic operators

Second degree partial differential equation with variable-change

Non-examples for the Kato-Rellich Theorem

Pair of PDEs to be solved together

Intuitive interpretation of $\frac{\partial S(a,t)}{\partial t} = -\frac{\partial S(a,t)}{\partial a}$

Local Mollification of a $L^1$ function

Solutions of a PDE in two dimensions

References on estimating capacities (Newton, Martin etc) for sets & alternative formulations.

Solving PDE via Fourier Transform & Uniqueness

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