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Topological properties of the solution set of a class of nonlinear evolutions inclusions

Nikolaos S. Papageorgiou (1997)

Czechoslovak Mathematical Journal

In the paper we study the topological structure of the solution set of a class of nonlinear evolution inclusions. First we show that it is nonempty and compact in certain function spaces and that it depends in an upper semicontinuous way on the initial condition. Then by strengthening the hypothesis on the orientor field F ( t , x ) , we are able to show that the solution set is in fact an R δ -set. Finally some applications to infinite dimensional control systems are also presented.

Topological tools for the prescribed scalar curvature problem on S n

Dina Abuzaid, Randa Ben Mahmoud, Hichem Chtioui, Afef Rigane (2014)

Open Mathematics

In this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

Total blow-up of a quasilinear heat equation with slow-diffusion for non-decaying initial data

Amy Poh Ai Ling, Masahiko Shimojō (2019)

Mathematica Bohemica

We consider solutions of quasilinear equations u t = Δ u m + u p in ℝ N with the initial data u 0 satisfying 0 < u 0 < M and lim | x | → ∞ u 0 ( x ) = M for some constant M > 0 . It is known that if 0 < m < p with p > 1 , the blow-up set is empty. We find solutions u that blow up throughout ℝ N when m > p > 1 .

Towards a two-scale calculus

Augusto Visintin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...

Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field L . Applications to the F. and M. Riesz property for vector fields are discussed.

Transition from decay to blow-up in a parabolic system

Pavol Quittner (1998)

Archivum Mathematicum

We show a locally uniform bound for global nonnegative solutions of the system u t = Δ u + u v - b u , v t = Δ v + a u in ( 0 , + ∞ ) × Ω , u = v = 0 on ( 0 , + ∞ ) × ∂ Ω , where a > 0 , b ≥ 0 and Ω is a bounded domain in ℝ n , n ≤ 2 . In particular, the trajectories starting on the boundary of the domain of attraction of the zero solution are global and bounded.

Currently displaying 181 – 200 of 219