numerical analysis of parabolic p laplacian approximation of trajectories the long time numerical approximation of the parabolic p laplacian problem with a time independent forcing term and sufficiently smooth initial data is studied convergence and stability results which are uniform for t in 0 infty are established in the l2 w1 p norms for the backward euler and the crank nicholson schemes with the finite element method fem this result extends the existing uniform convergence results for exponentially contractive semigroups generated by some semilinear systems to nonexponentially contractive semigroups generated by some quasi linear systems

quantum monodromy and nonconcentration near a closed semi hyperbolic orbit for a large class of semiclassical operators p h z which includes schrodinger operators on manifolds with boundary we construct the quantum monodromy operator m z associated to a periodic orbit of the classical flow using estimates relating m z and p h z we prove semiclassical estimates for small complex perturbations of p h z in the case is semi hyperbolic as our main application we give logarithmic lower bounds on the mass of eigenfunctions away from semi hyperbolic orbits of the associated classical flow as a second application of the monodromy operator construction we prove if is an elliptic orbit then p h admits quasimodes which are well localized near

periodic p laplacian with nonlocal terms abstract in this paper we study the existence of non trivial periodic solutions for a periodic p laplacian with nonlocal terms based on the theory of leray schauder degree the key step is dealing with the degeneracy of the p laplacian and the logistic type terms arising in the right hand side of the equation

on periodic solutions of superlinear parabolic problems on etudie l existence des solutions periodiques non triviales positives des problemes paraboliques semilineaires on demontre des resultats de bifurcation

corrigendum to semiclassical non concentration near hyperbolic orbits j funct anal 246 2 2007 145 195 doi 10 1016 j jfa 2006 09 012

homogeneous diffusion in ℝ with power like nonlinear diffusivity we study the nonnegative solutions of the initial value problem ut ur ux p 1ux x u x 0 l1 where p 0 r p 0 the local velocity of propagation of the solutions is identified as v vx vx p 1 where v cu with r p 1 p and c r p r p 1 is the nonlinear potential our main result is the a priori estimate vx vx p 1 x frac 1 2p r t

imperfect geometric control and overdamping for the damped wave equation we consider the damped wave equation on a manifold with imperfect geometric control we show the sub exponential energy decay estimate in christianson j funct anal 258 3 1060 1065 2010 is optimal in the case of one hyperbolic periodic geodesic we show if the equation is overdamped then the energy decays exponentially finally we show if the equation is overdamped but geometric control fails for one hyperbolic periodic geodesic then nevertheless the energy decays exponentially

existence uniqueness and numerical analysis of solutions of a quasilinear parabolic problem a quasilinear parabolic problem is studied by using the method of lines the existence and uniqueness of a solution to the initial boundary value problem with sufficiently smooth initial conditions are shown also given are l 2 error estimates for the error between the extended fully discrete finite element solutions and the exact solution

global solutions for some nonlinear parabolic equations with nonmonotonic peturbations publisher summary this chapter discusses the existence uniqueness and decay property of the solutions of two problems it also presents the sobolev s lemma and gagliardo nirenberg inequality

periodic solutions of non newtonian polytropic filtration equations with nonlinear sources in this paper the authors first consider the dirichlet boundary value problem to the non newtonian polytropic filtration equation of the form u t div u m p 2 u m h x t u a in wxrwith strong nonlinear sources the existence of nontrivial periodic solutions is established based on topological degree theory the authors also studied the dirichlet boundary value problem to the equation in the form u t div u m 1u p 2 u m 1u b x t u f x t in wxrwith weak nonlinear sources the existence is treated with leray schauder fixed point theory

existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms abstract in this paper the authors establish the existence of nontrivial nonnegative periodic solutions for a class of doubly degenerate parabolic equation with nonlocal terms by using the theory of leray schauder s degree

semiclassical non concentration near hyperbolic orbits for a large class of semiclassical pseudodifferential operators including schrodinger operators p h h2 g v x on compact riemannian manifolds we give logarithmic lower bounds on the mass of eigenfunctions outside neighbourhoods of generic closed hyperbolic orbits more precisely we show that if a is a pseudodifferential operator which is microlocally equal to the identity near the hyperbolic orbit and microlocally zero away from the orbit then u c log 1 h h p h u clog 1 h i a u this generalizes earlier estimates of colin de verdiere and parisse y colin de verdiere b parisse equilibre instable en regime semi classique i concentration microlocale comm partial differential equations 19 1994 1535 1563 equilibre instable en regime semi classique ii conditions de bohr sommerfeld ann inst h poincare phys theor 61 1994 347 367 obtained for a special case and of burq and zworski n burq m zworski geometric control in the presence of a black box j amer math soc 17 2004 443 471 for real hyperbolic orbits

holder estimates for local solutions of some doubly nonlinear degenerate parabolic equations abstract we prove interior and boundary holder continuity for bounded weak soluttions of a class of quasilinear parabolic equations whose prototype is u t div u m 1 du p 2 du

periodic solutions of evolutionp laplacian equations with nonlinear sources abstract in this paper we are concerned with the time periodic solutions to the evolution p laplacian equations of the form formula and formula with the dirichlet boundary value condition where p 2 0 is a bounded convex domain in r n with smooth boundary m x t is continuous on r periodic in t with period and positive in r the existence of nontrivial nonnegative periodic solutions is established provided that n 1 and p 1 p 1 p n