With the help of partial differential equations, a variety of processes from the natural sciences and even economics can be described. In realistic modelling, the differential equations are usually non-linear. Unlike linear partial differential equations, non-linear partial differential equations cannot be classified in a simple way. Therefore, many different special techniques are necessary to study the well-posedness of boundary value and initial boundary value problems and the qualitative behaviour of their solutions. In this lecture, typical strategies for semilinear and quasi-linear equations are presented.
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