ar X iv : 0 90 9 . 14 80 v 1 [ m at h . A P ] 8 S ep 2 00 9 ON QUASILINEAR PARABOLIC EVOLUTION EQUATIONS IN WEIGHTED L p - SPACES
نویسندگان
چکیده
In this paper we develop a geometric theory for quasilinear parabolic problems in weighted Lp-spaces. We prove existence and uniqueness of solutions as well as the continuous dependence on the initial data. Moreover, we make use of a regularization effect for quasilinear parabolic equations to study the ω-limit sets and the long-time behaviour of the solutions. These techniques are applied to a free boundary value problem. The results in this paper are mainly based on maximal regularity tools in (weighted) Lp-spaces.
منابع مشابه
ar X iv : 0 90 4 . 24 27 v 1 [ m at h . O C ] 1 6 A pr 2 00 9 Remarks on the Controllability of Some Quasilinear Equations ∗
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local controllability problem of quasilinear time-reversible evolution equations, which is based on a new unbounded perturbation technique. It is also worthy to mention th...
متن کاملar X iv : 0 90 6 . 14 58 v 1 [ m at h . A P ] 8 J un 2 00 9 DIFFERENCE - QUADRATURE SCHEMES FOR NONLINEAR DEGENERATE PARABOLIC INTEGRO - PDE
We derive and analyze monotone difference-quadrature schemes for Bellman equations of controlled Lévy (jump-diffusion) processes. These equations are fully non-linear, degenerate parabolic integro-PDEs interpreted in the sense of viscosity solutions. We propose new “direct” discretizations of the non-local part of the equation that give rise to monotone schemes capable of handling singular Lévy...
متن کاملar X iv : 0 90 5 . 16 85 v 1 [ m at h . A P ] 1 1 M ay 2 00 9 C 1 , α REGULARITY OF SOLUTIONS TO PARABOLIC MONGE - AMPÉRE EQUATIONS
We study interior C regularity of viscosity solutions of the parabolic Monge-Ampére equation ut = b(x, t) (detD u), with exponent p > 0 and with coefficients b which are bounded and measurable. We show that when p is less than the critical power 1 n−2 then solutions become instantly C in the interior. Also, we prove the same result for any power p > 0 at those points where either the solution s...
متن کاملar X iv : h ep - l at / 9 80 90 22 v 1 4 S ep 1 99 8 1 Hybrid and Orbitally Excited Mesons in Full QCD ∗
We present results for the hybrid meson spectrum produced by gluonic excitations in full QCD using Wilson fermions. For the spin-exotic mesons with J P C = 1 −+ , 0 +− , and 2 +− we find the lightest state to be 1 −+ with a mass of 1.9(2) GeV. Results obtained for orbitally excited mesons are also presented.
متن کاملar X iv : 0 80 9 . 05 00 v 1 [ m at h . FA ] 2 S ep 2 00 8 DIRECT LIMITS , MULTIRESOLUTION ANALYSES , AND WAVELETS
A multiresolution analysis for a Hilbert space realizes the Hilbert space as the direct limit of an increasing sequence of closed subspaces. In a previous paper, we showed how, conversely, direct limits could be used to construct Hilbert spaces which have multiresolution analyses with desired properties. In this paper, we use direct limits, and in particular the universal property which charact...
متن کامل