This  monograph  is  motivated  by  some  problems  from  Mathematical  Biology. Although  there  exists  an  extensive  literature  about  nonlinear  parabolic differential  equations,  none  of  the  known  results  could  be  used  to  prove global  existence  of  solutions  for  the  reaction-diffusion  systems  considered  in  this  monograph.  In  this  situation,  I  gave  an  ad  hoc  proof  of global existence  for  the  one-dimensional  reaction-diffusion  system  with reaction  A  +  B  ~  C subject  to  the  mass  action  law.  Afterwards  it  turned out  that  the  method used could  be  generalized  and  applied  to  other  problems  as  well.  For  the  time being,  the  subject  is  not  yet  exhausted. Further  interesting  examples  from  applications  are  needed  in  order  to build  a  substantial  theory  which  is  not  just  an  unnecessarily  abstract disguise  of  some  specific  problem.  The  author hopes  that  this  monograph will  be  useful  to  stimulate  research  in  this direction.

Global Solutions of Reaction-Diffusion Systems PDF

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