**5. Conclusion**

We investigate three different one-dimensional parabolic-parabolic Patlak-Keller-Segel models. For each of them, we obtain the exact solutions in terms of traveling wave variables. Not all of these solutions are acceptable for biological interpretation, but there are solutions that require detailed analysis. It seems interesting to consider the latter for the experimental values of the parameters and see their correspondence with experiment. This question requires further investigations.

**Author details**

**19**

Maria Vladimirovna Shubina

Moscow, Russian Federation

Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University,

*Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis*

*DOI: http://dx.doi.org/10.5772/intechopen.91214*

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*Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis DOI: http://dx.doi.org/10.5772/intechopen.91214*
