On the regularity of the variational solution of the Tricomi problem in the elliptic region
On the set of solutions of some nonconvex nonclosed hyperbolic differential inclusions
We consider a class of nonconvex and nonclosed hyperbolic differential inclusions and we prove the arcwise connectedness of the solution set.
On the solvability of a class of singular parabolic equations with nonlocal boundary conditions in nonclassical function spaces.
On the solvability of a nonlocal problem arising in dynamics of moisture transfer.
On the solvability of nonlocal pluriparabolic problems.
On the solvability of parabolic and hyperbolic problems with a boundary integral condition.
On the strong solution for the 3D stochastic Leray- model.
On the structure of solutions to elliptic problems with strong anisotropy.
On the uniformly continuity of the solution map for two dimensional wave maps.
On the uniqueness of viscosity solutions for first order partial differential-functional equations
We consider viscosity solutions for first order differential-functional equations. Uniqueness theorems for initial, mixed, and boundary value problems are presented. Our theorems include some results for generalized ("almost everywhere") solutions.
On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
On the weak solution of a three-point boundary value problem for a class of parabolic equations with energy specification.
On the well-posedness of some optimal control problems
Si considerano problemi di controllo ottimale con una dipendenza non lineare tra il controllo e lo stato. Si mostra come in certi casi la continuità di tale dipendenza, quindi la buona posizione nel senso di Tychonov, è connessa alla forma del funzionale costo. In particolare si esamina un problema di Stefan a due fasi con controllo distribuito nel termine di sorgente.
On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations.
Parabolic differential-functional inequalities in viscosity sense
We consider viscosity solutions for second order differential-functional equations of parabolic type. Initial value and mixed problems are studied. Comparison theorems for subsolutions, supersolutions and solutions are considered.
Parabolic equations with coefficients depending on t and parameters
Partial differential operators depending analytically on a parameter
Let be a differential operator with constant coefficients depending analytically on a parameter . Assume that the family P(,D) is of constant strength. We investigate the equation where is a given analytic function of with values in some space of distributions and the solution is required to depend analytically on , too. As a special case we obtain a regular fundamental solution of P(,D) which depends analytically on . This result answers a question of L. Hörmander.
Partial exact controllability of a nonlinear system.
In this article, we prove the partial exact controllability of a nonlinear system. We use semigroup formulation together with fixed point approach to study the nonlinear system.
Penalization of Dirichlet optimal control problems
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.
Penalization of Dirichlet optimal control problems
We apply Robin penalization to Dirichlet optimal control problems governed by semilinear elliptic equations. Error estimates in terms of the penalization parameter are stated. The results are compared with some previous ones in the literature and are checked by a numerical experiment. A detailed study of the regularity of the solutions of the PDEs is carried out.