Degenerate quasilinear evolution equations containing a volterra operator in the coefficients

Abstract EN

Conditions are established for solvability in the large of the first initial-boundary value problem in a bounded domain flcl" for the equation «,+(-ir I d° l« where q 3= 2 and \Dmu\2 |Dmu\qdt \Dmu\q~2 Dau = /, Yj \Dau\2.

It contains the integral of the unknown |o| =m function in the coefficients.

The problem is regarded as an evolution equation of the form u' +Au=f in the special space Lq(0,T)).

It is proved that the evolution equation is solvable under the additional assumptions that the function 0(5) is monotonically increasing and concave, but not necessarily differentiable.