Parbolic pseudo-differential initial-boundary value problems.
Let E be a Banach space. We consider a Cauchy problem of the type ⎧ in , ⎨ ⎩ in , j=0,...,k-1, where each is a given continuous linear operator from E into itself. We prove that if the operators are nilpotent and pairwise commuting, then the problem is well-posed in the space of all functions whose derivatives are equi-bounded on each bounded subset of .
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.
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.
Sfruttando i risultati di [1], si prova che le derivate spaziali di ordine con delle soluzioni in di un sistema parabolico quasilineare di ordine con andamenti strettamente controllati, sono parzialmente hölderiane in con esponente di hölderianità decrescente al crescere di .