List questions from fundamental-solution

Published on 25 Mar 2026 - 10:21

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Solving Laplacian in $\mathbb{R}^2$

Published on 14 May 2023 - 14:37

223

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General solution of $x^2 u_{xx} - 2xy u_{xy} + y^2 u_{yy} = e^x$

Published on 15 May 2023 - 17:35

235

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On the solution of the heat equation using distribution theory

Published on 17 May 2023 - 9:19

182

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Fundamental Solution of a heat equation with a drift term

Published on 23 May 2023 - 9:03

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Exactly one homogeneous differential equation of second order to given fundamental solution

Published on 23 Feb 2026 - 10:18

161

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Finding solution of non-homogeneous ODE when we know the solutions of the homogeneous counterpart

Published on 21 Aug 2023 - 12:57

40

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Is this the fundamental solution?

Published on 06 Sep 2023 - 22:27

83

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Show that $\frac 1{4\pi |x|} e^{-c|x|}$ is a fundamental solution for $-\Delta+c^2$ on $\mathbb R^3$

Published on 05 Oct 2023 - 13:00

70

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Verification of the formula of variation of parameters for ODE

Published on 29 Oct 2023 - 8:19

35

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Show that $\lim_{\tau \to t}\int_\Omega \Phi(x-\xi, t-\tau)u(\xi,\tau)d\xi = u(x,t)$

Published on 09 Dec 2023 - 0:07

44

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Fundamental matrix of $x'= (-1+\frac{3}{2}\cos^2t)x+(1-\frac{3}{2}\sin t\cos t)y,~y'=(-1-\frac{3}{2}\sin t \cos t)x+(-1+\frac{3}{2}\sin^2t) y$

Published on 19 Dec 2023 - 12:55

59

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Fundamental matrix solution remains invertible

Published on 25 Dec 2023 - 18:37

80

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Deriving the fundamental solution to heat equation

Published on 08 Jan 2024 - 15:37

50

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Constant Coefficient Operators: Fundamental solution of Cauchy-Riemann Operator - Folland, Introduction to PDE

Published on 28 Jan 2024 - 23:44

List Question

What is a distinct feature of an ambiguous result

Solving Laplacian in $\mathbb{R}^2$

General solution of $x^2 u_{xx} - 2xy u_{xy} + y^2 u_{yy} = e^x$

On the solution of the heat equation using distribution theory

Fundamental Solution of a heat equation with a drift term

Exactly one homogeneous differential equation of second order to given fundamental solution

Finding solution of non-homogeneous ODE when we know the solutions of the homogeneous counterpart

Is this the fundamental solution?

Show that $\frac 1{4\pi |x|} e^{-c|x|}$ is a fundamental solution for $-\Delta+c^2$ on $\mathbb R^3$

Verification of the formula of variation of parameters for ODE

Show that $\lim_{\tau \to t}\int_\Omega \Phi(x-\xi, t-\tau)u(\xi,\tau)d\xi = u(x,t)$

Fundamental matrix of $x'= (-1+\frac{3}{2}\cos^2t)x+(1-\frac{3}{2}\sin t\cos t)y,~y'=(-1-\frac{3}{2}\sin t \cos t)x+(-1+\frac{3}{2}\sin^2t) y$

Fundamental matrix solution remains invertible

Deriving the fundamental solution to heat equation

Constant Coefficient Operators: Fundamental solution of Cauchy-Riemann Operator - Folland, Introduction to PDE

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