×

Dispersal models. (English) Zbl 0795.92029

Some models of insect dispersal are presented. In the particular case \[ \partial u/\partial t=-D_ 2\Delta^ 4u+D_ 0\Delta\bigl((u/u_ 0)^ m\Delta u\bigr), \] where \(u\) represents the population density, \(D_ 0\), \(u_ 0\), \(D_ 2\), \(m\) are positive constants \((u_ 0\) is a reference concentration, \(D_ 0\) is a diffusion coefficient for \(u=u_ 0\), \(D_ 2\) is a measure of the long range effects), the authors prove the existence and uniqueness of weak global solutions, with the initial condition \(u(x,0) = g(x)\), \(g(x) \in L^ m(R^ 2)\).

MSC:

92D40 Ecology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35K30 Initial value problems for higher-order parabolic equations
PDFBibTeX XMLCite