On quasilinear parabolic equations and continuous maximal regularity

2018/08/02 by LeCrone, Jeremy, Simonett, Gieri
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.01032

Abstract

We consider a class of abstract quasilinear parabolic problems with lower--order terms exhibiting a prescribed singular structure. We prove well--posedness and Lipschitz continuity of associated semiflows. Moreover, we investigate global existence of solutions and we extend the generalized principle of linearized stability to settings with initial values in critical spaces. These general results are applied to the surface diffusion flow in various settings.

Related

• On the regularity theory for mixed local and nonlocal quasilinear parabolic equations
• Quasilinear parabolic equations with superlinear nonlinearities in critical spaces
• Quasi-linear parabolic equations having a superlinear gradient term which depends on the solution
• On quasilinear parabolic evolution equations in weighted Lp-spaces II
• Parabolic equations with dynamical boundary conditions and source terms on interfaces