Math Help - Semilinear Wave Equation - White Noise

1. Semilinear Wave Equation - White Noise

Hello!

I am required to do a paper on the Semilinear Wave Equation as part of a Stochastic Partial Differential Equations seminar.
The problem is, that I've never taken a course on partial differential equations (only ordinary differential equations) or functional analysis.

Now I have the following in front of me:

Let $f(s,x,t)$ and $\sigma(s,x,t)$ be predictable random fields
depending on the parameters $s\in\mathbf{R}$ and $x\in D$. We consider
the initial-boundary value problems for a stochastic wave equation
as follows

$\frac{\partial^{2}u}{\partial t^{2}}=(\kappa\Delta-\alpha)u+f(u,x,t)+\dot{M}(u,x,t)$
$x\in D$, $t\in(0,T]$

$Bu$| $_{\partial D}=0$

$u(x,0)=g(x),$ $\frac{\partial u}{\partial t}(x,0)=h(x)$

where

$\dot{M}(s,x,t)=\sigma(s,x,t)\dot{W}(x,t)$

My problem is now, that I don't understand how this second order differential was constructed.
What are $(\kappa\Delta-\alpha)u$, $f(u,x,t)$, $\dot{M}(u,x,t)$ supposed to be here and what has this to do with waves?

Thank you for your time.
If you can pinpoint me to some resources, which will make my life easier in understanding this. I will be very thankful!

2. Originally Posted by NoClue
Hello!

I am required to do a paper on the Semilinear Wave Equation as part of a Stochastic Partial Differential Equations seminar.
The problem is, that I've never taken a course on partial differential equations (only ordinary differential equations) or functional analysis.

Now I have the following in front of me:

Let $f(s,x,t)$ and $\sigma(s,x,t)$ be predictable random fields
depending on the parameters $s\in\mathbf{R}$ and $x\in D$. We consider
the initial-boundary value problems for a stochastic wave equation
as follows

$\frac{\partial^{2}u}{\partial t^{2}}=(\kappa\Delta-\alpha)u+f(u,x,t)+\dot{M}(u,x,t)$
$x\in D$, $t\in(0,T]$

$Bu$| $_{\partial D}=0$

$u(x,0)=g(x),$ $\frac{\partial u}{\partial t}(x,0)=h(x)$

where

$\dot{M}(s,x,t)=\sigma(s,x,t)\dot{W}(x,t)$

My problem is now, that I don't understand how this second order differential was constructed.
What are $(\kappa\Delta-\alpha)u$, $f(u,x,t)$, $\dot{M}(u,x,t)$ supposed to be here and what has this to do with waves?

Thank you for your time.
If you can pinpoint me to some resources, which will make my life easier in understanding this. I will be very thankful!
Why are you attending this seminar when your pre-requisite background is so deficient?

3. Hello chum !

I had no alternatives. I was away when the topics for the different seminars were handed out. I had other favorites, but they were already booked out .
I literally had nothing else to choose from...

I am reading Oksendals book on SPDE's and am trying to catch up by myself...

However, I am very thankful, if someone would show me what to do (what material to work through), so I can quickly get to my topic.