5 papers · 2 filters
On the principle of linearized stability for quasilinear evolution equations in time-weighted spaces
Bogdan-Vasile Matioc, Lina Sophie Schmitz, Christoph Walker
Quasilinear (and semilinear) parabolic problems of the form with strict inclusion of the domains of the function $v\maps…
Quasilinear parabolic equations with superlinear nonlinearities in critical spaces
Bogdan-Vasile Matioc, Luigi Roberti, Christoph Walker
Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations is established in a certain critical case of strict inclusion…
Recovering Initial States in Semilinear Parabolic Problems from Time-Averages
Lina Sophie Schmitz, Christoph Walker
Well-posedness of certain semilinear parabolic problems with nonlocal initial conditions is shown in time-weighted spaces. The result is applied to recover the initial states in se…
Global solutions for semilinear parabolic evolution problems with Hölder continuous nonlinearities
Bogdan-Vasile Matioc, Christoph Walker
It is shown that semilinear parabolic evolution equations featuring Hölder continuous nonlinearities with at most linear growth possess global strong solu…
On a Quasilinear Parabolic-Hyperbolic System Arising in MEMS Modeling
Christoph Walker
A coupled system consisting of a quasilinear parabolic equation and a semilinear hyperbolic equation is considered. The problem arises as a small aspect ratio limit in the modeling…