Found 2 essays containing the words Karoline Johansson.

1. ## 1. Municipal solid waste management in Minsk - current situation, future development and challenges

University essay from Lunds universitet/Miljövetenskaplig utbildning

Abstract : Management of municipal solid waste (MSW) is an urgent issue throughout the world. Urbanization, population increase, and economy growth are all factors which contribute to an increase of MSW generation. READ MORE

2. ## 2. A counterexample concerning nontangential convergence for the solution to the time-dependent Schrödinger equation

University essay from Växjö universitet/Matematiska och systemtekniska institutionen

Abstract : Abstract: Considering the Schrödinger equation $\Delta_x u = i\partial{u}/\partial{t}$, we have a solution $u$ on the form $$u(x, t)= (2\pi)^{-n} \int_{\RR} {e^{i x\cdot \xi}e^{it|\xi|^2}\widehat{f}(\xi)}\, d \xi, x \in \RR, t \in \mathbf{R}$$ where $f$ belongs to the Sobolev space. It was shown by Sjögren and Sjölin, that assuming $\gamma : \mathbf{R}_+ \rightarrow \mathbf{R}_+$ being a strictly increasing function, with $\gamma(0) = 0$ and $u$ and $f$ as above, there exists an $f \in H^{n/2} (\RR)$ such that $u$ is continuous in $\{ (x, t); t>0 \}$ and $$\limsup_{(y,t)\rightarrow (x,0),|y-x|<\gamma (t), t>0} |u(y,t)|= + \infty$$ for all $x \in \RR$. READ MORE