arXiv subjects

Théo Belin

Publications and source records attributed to Théo Belin.

3 recordsLinked to original sources

arXiv2026

A Ginzburg-Landau approximation theorem for quasilinear pattern-forming systems in uniformly local Sobolev spaces

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear or fully nonlinear pattern-forming systems close to the first instability. We present an approximation theory in uniform local Sobolev spaces which is applied to a quasilinear Swift-Hohenberg model, to a quasilinear version of Bénard's problem with velocity dependent viscosity, and to abstract quasilinear reaction-diffusion-advection systems.

math.AP↗

arXiv2026

On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems

We prove that the Ginzburg-Landau equation correctly predicts the dynamics of quasilinear pattern-forming reaction-diffusion-advection systems, close to the first instability. We present a simple theorem which is easily applicable for such systems and relies on key maximal regularity results. The theorem is applied to the Gray-Scott-Klausmeier vegetation-water interaction model and its application to general reaction-diffusion-advection systems is discussed.

math.AP↗

arXiv2024

Quantitative estimates of $L^p$ maximal regularity for nonautonomous operators and global existence for quasilinear equations

In this work, we obtain quantitative estimates of the continuity constant for the $L^p$ maximal regularity of relatively continuous nonautonomous operators $\mathbb{A} : I \longrightarrow \mathcal{L}(D,X)$, where $D \subset X$ densely and compactly. They allow in particular to establish a new general growth condition for the global existence of strong solutions of Cauchy problems for nonlocal quasilinear equations for a certain class of nonlinearities $u \longrightarrow \mathbb{A}(u)$. The estimates obtained rely on the precise asymptotic analysis of the continuity constant with respect to perturbations of the operator of the form $\mathbb{A}(\cdot) + λI$ as $λ\longrightarrow \pm \infty$. A complementary work in preparation supplements this abstract inquiry with an application of these results to nonlocal parabolic equations in noncylindrical domains depending on the time variable.

math.FA↗