List questions from partial-differential-equations

Published on 25 Mar 2026 - 13:53

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Integrals of motion remain constant (proof)

Published on 05 Apr 2026 - 20:03

295

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Help with PDE $xu_x+yu_y=2u$

Published on 25 Mar 2026 - 15:59

326

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Solution of $\nabla^2u=u_{xx}+u_{yy}=0$?

Published on 26 Mar 2026 - 6:05

391

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What is closed form solution (if there is any) to this PDE :

Published on 31 May 2018 - 0:11

196

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If $I = \int_{-\infty}^\infty(xu - 3tu^2)\mathrm{d}x$, show that $\frac{\mathrm{d}I}{\mathrm{d}t} = 0$.

Published on 27 Mar 2026 - 23:48

560

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If $f(x) = e^{-|x|}$, show that $f''(x) - f(x) = -2\delta(x)$ (in the sense of distributions)

Published on 25 Mar 2026 - 6:30

24

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Help understand the solution of a difference equation.

Published on 31 May 2018 - 21:44

109

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PDE IVP : $\Delta u(x,y)=e^{-x^4-y^4}, \; \; u_y(x,0) = e^{-|x|}\sin(x)$

Published on 25 Mar 2026 - 4:40

262

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Finding the integrating factor for an ODE through the PDE characterisitc method

Published on 25 Mar 2026 - 15:58

569

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Heat equation using the Laplace Transform

Published on 25 Mar 2026 - 6:09

872

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Is the solution of $ u_{tt}=c^2u_{xx}+xt $ correct?

Published on 25 Mar 2026 - 1:16

618

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How to derive the representation formula from $\mathbb R^3$ to $\mathbb R^2$?

Published on 25 Mar 2026 - 12:48

192

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PDE IVP : $zz_x + z_y = 0, \; \; z(x,0) = -3x$

Published on 25 Mar 2026 - 2:12

233

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PDE : $x^2 z_x + y^2 z_y = z(x+y)$

Published on 01 Jun 2018 - 10:48

List Question

Proof request - Lemma (Non-continuous ODE solutions of $u_t + A(u)_x = 0$

Integrals of motion remain constant (proof)

Help with PDE $xu_x+yu_y=2u$

Solution of $\nabla^2u=u_{xx}+u_{yy}=0$?

What is closed form solution (if there is any) to this PDE :

If $I = \int_{-\infty}^\infty(xu - 3tu^2)\mathrm{d}x$, show that $\frac{\mathrm{d}I}{\mathrm{d}t} = 0$.

If $f(x) = e^{-|x|}$, show that $f''(x) - f(x) = -2\delta(x)$ (in the sense of distributions)

Help understand the solution of a difference equation.

PDE IVP : $\Delta u(x,y)=e^{-x^4-y^4}, \; \; u_y(x,0) = e^{-|x|}\sin(x)$

Finding the integrating factor for an ODE through the PDE characterisitc method

Heat equation using the Laplace Transform

Is the solution of $ u_{tt}=c^2u_{xx}+xt $ correct?

How to derive the representation formula from $\mathbb R^3$ to $\mathbb R^2$?

PDE IVP : $zz_x + z_y = 0, \; \; z(x,0) = -3x$

PDE : $x^2 z_x + y^2 z_y = z(x+y)$

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