Multidimensional Scalar Conservation Laws
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Our analysis has so far been confined to scalar conservation laws in one dimension. Clearly, the multidimensional case is considerably more important. Luckily enough, the analysis in one dimension can be carried over to higher dimensions by essentially treating each dimension separately. This technique is called dimensional splitting. The final results are very much the natural generalizations one would expect.
The same splitting techniques of dividing complicated differential equations into several simpler parts can in fact be used to handle other problems. These methods are generally called operator splitting methods or fractional steps methods.