Dietrich Häfner, Cécile Huneau. Source: Advances in Differential Equations, Volume 24, Number 7/8, 435--464.Abstract: We consider the spherically symmetric $SU(2)$ Yang-Mills fields on the Schwarzschild metric. Within the so called purely magnetic Ansatz, we show that there exists a countable...

F. Crispo, P. Maremonti, M. Růžička. Source: Advances in Differential Equations, Volume 24, Number 7/8, 407--434.Abstract: We consider the initial boundary value problem for the $p(t,x)$-Laplacian system in a bounded domain $\Omega$. If the initial data belongs to $L^{r_0}$, $r_0\geq 2$, we prove...

Robert Denk, Felix Hummel. Source: Advances in Differential Equations, Volume 24, Number 7/8, 377--406.Abstract: We study dispersive mixed-order systems of pseudodifferential operators in the setting of $L^p$-Sobolev spaces. Under the weak condition of quasi-hyperbolicity, these operators generate...

Katsunori Gunji. Source: Advances in Differential Equations, Volume 24, Number 5/6, 321--376.Abstract: Knot energies, one of which is the Möbius energy, are constructed to measure the well-proportioned of the knot. The best-proportioned knot in the given knot class may be determined by the...

Hartmut Pecher. Source: Advances in Differential Equations, Volume 24, Number 5/6, 283--320.Abstract: We prove that the Yang-Mills equation in Lorenz gauge in the (n+1)-dimensional case, $n \ge 4$, is locally well-posed for data of the gauge potential in $H^s$ and the curvature in $H^r$, where $s...

Mathias Nikolai Arnesen. Source: Advances in Differential Equations, Volume 24, Number 5/6, 257--282.Abstract: We consider the Cauchy problem \[ \partial_t u+u\partial_x u+L(\partial_x u) =0, \quad u(0,x)=u_0(x) \] for a class of Fourier multiplier operators $L$, and prove that the solution map...

Davide Addona, Luciana Angiuli, Luca Lorenzi. Source: Advances in Differential Equations, Volume 24, Number 3/4, 137--184.Abstract: In this paper, we deal with weakly coupled elliptic systems ${\mathcal A}$ with unbounded coefficients. We prove the existence and characterize all the systems of...

Yingying Liu, Zhengce Zhang, Liping Zhu. Source: Advances in Differential Equations, Volume 24, Number 3/4, 229--256.Abstract: This paper deals with a quasilinear parabolic equation with nonlinear gradient absorption \begin{equation*} u_t-\Delta_{p}u=u^q-\mu u^{r}|\nabla u|^\delta, \ x\in\Omega,...

Alberto Lastra, Stéphane Malek. Source: Advances in Differential Equations, Volume 24, Number 1/2, 69--136.Abstract: We consider a nonlinear singularly perturbed PDE leaning on a complex perturbation parameter $\epsilon$. The problem possesses an irregular singularity in time at the origin and...

Yasuhide Fukumoto, Xiaopeng Zhao. Source: Advances in Differential Equations, Volume 24, Number 1/2, 31--68.Abstract: In this paper, the properties of weak and strong solutions for the Hall-magnetohydrodynamic system augmented by the effect of electron inertia are studied. First, we establish the...