Abstract In this paper, we are interested in $L^{\infty }$ L ∞ decay estimates of weak solutions for the doubly nonlinear parabolic equation and degenerate evolution m -Laplacian not divergence form. By a modified Moser’s technique obtain solutiona.

We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system ∫ ΩT ( u · φt − |Dmu|p−2Dmu ·Dmφ ) dz = ∫

in this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,t)$, subject to nulldirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. the optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

We study the inverse problem of recovering source function in a degenerate parabolic equation with many spatial variables. An additional integral observation condition is imposed. find sufficient conditions for unique solvability cases where unknown looked space L2(0, T) or L∞(0, T). The results obtained are based on preliminary corresponding direct which independent interest.

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Mathias Masson Name of the doctoral dissertation Regularity for parabolic quasiminimizers in metric measure spaces Publisher School of Science Unit Department of Mathematics and Systems Analysis Series Aalto University publication series DOCTORAL DISSERTATIONS 89/2013 Field of research Mathematical analysis Manuscript submitte...