Global bounds for cocoercive variational inequalities.
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
Global existence and nonexistence for semiliniear parabolic systems with nonlinear boundary conditions.
Global Existence and Stability for Neutral Functional Evolution Equations with State-Dependent Delay
In this paper we prove the global existence and attractivity of mild solutions for neutral semilinear evolution equations with state-dependent delay in a Banach space.
Global existence for a Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.
Global existence for a semilinear prabolic Volterra equation.
Global existence for coupled Klein-Gordon equations with different speeds
Consider, in dimension 3, a system of coupled Klein-Gordon equations with different speeds, and an arbitrary quadratic nonlinearity. We show, for data which are small, smooth, and localized, that a global solution exists, and that it scatters. The proof relies on the space-time resonance approach; it turns out that the resonant structure of this equation has features which were not studied before, but which are generic in some sense.
Global existence for semilinear parabolic systems.
Global existence for the Hamilton-Jacobi equations in Hilbert space
Global existence, uniqueness, and continuous dependence for a reaction-diffusion equation with memory.
Global minimizer of the ground state for two phase conductors in low contrast regime
The problem of distributing two conducting materials with a prescribed volume ratio in a ball so as to minimize the first eigenvalue of an elliptic operator with Dirichlet conditions is considered in two and three dimensions. The gap ε between the two conductivities is assumed to be small (low contrast regime). The main result of the paper is to show, using asymptotic expansions with respect to ε and to small geometric perturbations of the optimal shape, that the global minimum of the first eigenvalue...
Global Poissonian behavior of the eigenvalues and localization centers of random operators in the localized phase
In the present note, we review some recent results on the spectral statistics of random operators in the localized phase obtained in [12]. For a general class of random operators, we show that the family of the unfolded eigenvalues in the localization region considered jointly with the associated localization centers is asymptotically ergodic. This can be considered as a generalization of [10]. The benefit of the present approach is that one can vary the scaling of the unfolded eigenvalues covariantly...
Global properties of components of solutions of non-linear second order ordinary differential equations on the half-line
Global Properties of the Minimal Branch of a Class of Nonlinear Variational Problems.
Global Schauder estimates for a class of degenerate Kolmogorov equations
We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...
Global Several-Parameter Bifurcation and Continuation Theorems: a UnifiedApproach Via Complementing Maps.
Global smooth solutions to a class of semilinear wave equations with strong nonlinearities.
Global solutions for a functional second order abstract Cauchy problem with nonlocal conditions
By using the theory of strongly continuous cosine families and the properties of completely continuous maps, we study the existence of mild, strong, classical and asymptotically almost periodic solutions for a functional second order abstract Cauchy problem with nonlocal conditions.
Global solutions for abstract functional differential equations with nonlocal conditions.
Global solutions of semilinear heat equations in Hilbert spaces.