Existence and nonexistence of global solutions of degenerate and singular parabolic systems.
Existence and stability of asymptotically oscillatory double pulses.
Full regularity of bounded solutions to nondiagonal parabolic systems of two equations
Hölder continuity and, basing on this, full regularity and global existence of weak solutions is studied for a general nondiagonal parabolic system of nonlinear differential equations with the matrix of coefficients satisfying special structure conditions and depending on the unknowns. A technique based on estimating a certain function of unknowns is employed to this end.
Global existence and blow-up for a completely coupled Fujita type system
The Fujita type global existence and blow-up theorems are proved for a reaction-diffusion system of m equations (m>1) in the form
Interior differentiability of weak solutions to parabolic systems with quadratic growth nonlinearities
-stability of multi-solitons
The aim of this note is to give a short review of our recent work (see [5]) with Miguel A. Alejo and Luis Vega, concerning the -stability, and asymptotic stability, of the -soliton of the Korteweg-de Vries (KdV) equation.
regularity for weak solutions of parabolic systems
Local solvability of diagonal semilinear parabolic systems
Maximum principles for parabolic systems coupled in both first-order and zero-order terms.
On Fenchel dual schemes in convex optimal control problems
On reaction-diffusion systems.
On the existence of two-dimensional invariant tori for scalar parabolic equations with time periodic coefficients
On the Hölder continuity of solutions of nonlinear parabolic systems
Non-linear second order parabolic systems in the divergent form are considered. It is proved that under some restrictions on the modulus of ellipticity, all weak solutions are continuous.
On the Hölder continuity of weak solutions to nonlinear parabolic systems in two space dimensions
We prove the interior Hölder continuity of weak solutions to parabolic systems (), where the coefficients are measurable in , Hölder continuous in and Lipschitz continuous in and .
On the local integrability and boundedness of solutions to quasilinear parabolic systems.
Oscillation criteria for nonlinear inhomogeneous hyperbolic equations with distributed deviating arguments.
Parabolic equations with multiple singularities
Partial Hölder continuity for quasilinear parabolic systems of higher order with strictly controlled growth
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 .
PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages
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...
PDE-constrained optimization of time-dependent 3D electromagnetic induction heating by alternating voltages
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...