Global existence and asymptotic behavior of solutions for the Klein-Gordon equations with quadratic nonlinearity in two space dimensions.
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 Instability and Essential Spectrum in Semilinear Evolution Equations.
Global solution to the Cauchy problem of nonlinear thermodiffusion in a solid body
We consider the initial-value problem for a nonlinear hyperbolic-parabolic system of three coupled partial differential equations of second order describing the process of thermodiffusion in a solid body (in one-dimensional space). We prove global (in time) existence and uniqueness of the solution to the initial-value problem for this nonlinear system. The global existence is proved using time decay estimates for the solution of the associated linearized problem. Next, we prove an energy estimate...
Global well-posedness for the Klein-Gordon-Schrödinger system with higher order coupling
Global well-posedness for the Klein-Gordon-Schrödinger system with generalized higher order coupling, which is a system of PDEs in two variables arising from quantum physics, is proven. It is shown that the system is globally well-posed in under some conditions on the nonlinearity (the coupling term), by using the conservation law for and controlling the growth of via the estimates in the local theory. In particular, this extends the well-posedness results for such a system in Miao, Xu (2007)...
Global well-posedness of the Cauchy problem of a higher-order Schrödinger equation.
G-сходимость одного класса эволюционных операторов
Hard implicit function theorem and small periodic solutions to partial differential equations
Harnack inequalities for evolving hypersurfaces.
Higher asymptotics of the complex Monge-Ampère equation
Higher integrability for weak solutions of higher order degenerate parabolic systems.
High-order mixed-type differential equations with weighted integral boundary conditions.
Hölder regularity in non autonomous degenerate abstract parabolic equations
Homogeneous two-point problem for PDE of the second order in time variable and infinite order in spatial variables
We prove that homogeneous problem for PDE of second order in time variable, and generally infinite order in spatial variables with local two-point conditions with respect to time variable, has only trivial solution in the case when the characteristic determinant of the problem is nonzero. In another, opposite case, we prove the existence of nontrivial solutions of the problem, and we propose a differential-symbol method of constructing them.
How many are affine connections with torsion
The question how many real analytic affine connections exist locally on a smooth manifold of dimension is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.
How many are equiaffine connections with torsion
The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold of dimension is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of variables.
Hypoellipticité d'équations aux dérivées partielles non linéaires
Hypoellipticité et hyperfonctions
Identifiability for a class of discretized linear partial differential algebraic equations.
Implicit second order partial differential equations