Sfruttando i risultati di [1], si prova che le derivate spaziali $D^{\alpha }u$ di ordine $|\alpha |$ con delle soluzioni in $Q$ di un sistema parabolico quasilineare di ordine $2m$ con andamenti strettamente controllati, sono parzialmente hölderiane in $Q$ con esponente di hölderianità decrescente al crescere di $|\alpha |$.

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

This paper is concerned with a PDE-constrained optimization problem of induction heating, where the state equations consist of 3D time-dependent heat equations coupled with 3D time-harmonic eddy current equations. The control parameters are given by finite real numbers representing applied alternating voltages which enter the eddy current equations via impressed current. The optimization problem is to find optimal voltages so that, under certain constraints on the voltages and the temperature, a...

De tels problèmes mixtes sont étudiés dans certains domaines non cylindriques, lorsque les conditions à l’instant initial sont celles de Cauchy, par l’intermédiaire de problèmes pseudo-différentiels sur le bord latéral du domaine. On donne des conditions qui permettent d’établir l’existence ou l’unicité de la solution.