# Questions tagged [inverse-laplace]

This tag is for questions regarding to "Inverse Laplace Transform" which is the transformation of a Laplace transform into a function of time.

272 questions
Filter by
Sorted by
Tagged with
22 views

12 views

### Bromwich contour of inverse transform

I have a given equation $$F(s)=b/(s-a)^2+b^2$$ where a and b are real numbers. While I was able to find two roots which are $$sqrt(a)$$ and $$-sqrt(a)$$. However I am stuck on algebra part, where I ...
35 views

### Find the inverse laplace transform of $\mathcal{L^{-1}}$

If $\mathcal{L^{-1}}=\frac{2-2e^{-5s}}{s(s+1)^2}+\frac{e^{-6s}}{(s+1)^2}$, how do I find the inverse Laplace transform? I see that there are fractions for this equation, so I have to use partial ...
18 views

### How to obtain the pole and the order of a complex function with a quotient of Bessel functions

I am trying to determine the Inverse Laplace Transformation of the following function. \begin{equation} p(\zeta) = \ \frac{ K\sqrt{{I_{2}{(\sqrt{\zeta})}}}} { \sinh\left[\sqrt{\frac{I_{0}{(\sqrt{\...
49 views

### Find the inverse laplace transforms of $\frac{\ln(s)}{s^2}$

I have the equation $\mathcal{L}^{-1}=\frac{\ln(s)}{s^2}$. How do I find the Laplace inverse transform? I know that $\mathcal{L}[\ln(t)]=-\frac{1}{s}(\gamma+\ln(s))$, so I need to probably transform ...
54 views

### Inverse Laplace transform (double integral)

Is it possible to find a function $F:\mathbb R^+\times \mathbb R^+\to\mathbb R$ such that \begin{align} \int_0^\infty\int_0^\infty F(x,y)e^{-xq-yq}dxdy=\frac{\alpha}{q^4}+\frac{\beta}{q^3}+\frac{\...
15 views

292 views

### Is the reciprocal of the inverse tangent function, $\frac1{\arctan x}$, a (logarithmically) completely monotonic function on $(0,\infty)$?

A non-negative function $f$ is said to be completely monotonic on an interval $I$ if $f$ has derivatives of all orders on $I$ and \begin{equation*} 0\le(-1)^{n-1}f^{(n-1)}(x)<\infty \end{equation*} ...
43 views

### Using the theorem of convolution find the inverse Laplace transform

Using the theorem of convolution find the inverse Laplace transform: \begin{align} F(s)=\frac{s}{(s-1)(s+2)}\end{align} This is what I have so far: \begin{align} Let \space F_1(s)=\frac{s}{s-1} and\...
36 views

### Is the inverse Laplacian bounded in $\mathbb{R}^{2}$?

I'm searching for an inequality in the form $$\forall s>2,\quad\forall u\in H^{s-2}(\mathbb{R}^{2}),\quad\|\Delta^{-1}u\|_{H^{s}(\mathbb{R}^{2})}\lesssim\|u\|_{H^{s-2}(\mathbb{R}^{2})}$$ where $H^s$...
15 views

### Inverse Laplace transform of inverse function containing logarithm

I am trying to find the inverse Laplace transform of the following function but am currently stumped. My understanding is that I can't formally solve the integral because of the singularity at $s=0$, ...