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Solvability for semilinear PDE with multiple characteristics

Alessandro Oliaro, Luigi Rodino (2003)

Banach Center Publications

We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in G σ , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class G σ with respect to all variables.

Solvability near the characteristic set for a class of planar vector fields of infinite type

Alberto P. Bergamasco, Abdelhamid Meziani (2005)

Annales de l’institut Fourier

We study the solvability of equations associated with a complex vector field L in ℝ 2 with C ∞ or C ω coefficients. We assume that L is elliptic everywhere except on a simple and closed curve Σ . We assume that, on Σ , L is of infinite type and that L ∧ L ¯ vanishes to a constant order. The equations considered are of the form L u = p u + f , with f satisfying compatibility conditions. We prove, in particular, that when the order of vanishing of L ∧ L ¯ is &gt; 1 , the equation L u = f is solvable in the C ∞ category but not in the C ω category....

Solvability of a class of phase field systems related to a sliding mode control problem

Michele Colturato (2016)

Applications of Mathematics

We consider a phase-field system of Caginalp type perturbed by the presence of an additional maximal monotone nonlinearity. Such a system arises from a recent study of a sliding mode control problem. We prove the existence of strong solutions. Moreover, under further assumptions, we show the continuous dependence on the initial data and the uniqueness of the solution.

Solvability of a dynamic rational contact with limited interpenetration for viscoelastic plates

Jiří Jarušek (2020)

Applications of Mathematics

Solvability of the rational contact with limited interpenetration of different kind of viscolastic plates is proved. The biharmonic plates, von Kármán plates, Reissner-Mindlin plates, and full von Kármán systems are treated. The viscoelasticity can have the classical (``short memory'') form or the form of a certain singular memory. For all models some convergence of the solutions to the solutions of the Signorini contact is proved provided the thickness of the interpenetration tends to zero.

Solvability of a first order system in three-dimensional non-smooth domains

Michal Křížek, Pekka Neittaanmäki (1985)

Aplikace matematiky

A system of first order partial differential equations is studied which is defined by the divergence and rotation operators in a bounded nonsmooth domain Ω ⊂ 𝐑 3 . On the boundary δ Ω , the vanishing normal component is prescribed. A variational formulation is given and its solvability is investigated.

Solvability of invariant sublaplacians on spheres and group contractions

Fulvio Ricci, Jérémie Unterberger (2001)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In the first part of this paper we study the local and global solvability and the hypoellipticity of a family of left-invariant sublaplacians L α on the spheres S 2 ⁢ n + 1 ≃ U ⁢ n + 1 / U ⁢ n . In the second part, we introduce a larger family of left-invariant sublaplacians L α , β on S 3 ≃ S ⁢ U ⁢ 2 and study the corresponding properties by means of a Lie group contraction to the Heisenberg group.

Currently displaying 581 – 600 of 1682