The Allen–Cahn equation with generic initial datum

On power series solutions for the Euler equation, and the Behr-Nečas-Wu initial datum

Carlo Morosi , Mario Pernici , Livio Pizzocchero c () a Dipartimento di Matematica, Politecnico di Milano, P.za L. da Vinci 32, I-20133 Milano, Italy e–mail: [email protected] b Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Via Celoria 16, I-20133 Milano, Italy e–mail: [email protected] c Dipartimento di Matematica, Università di Milano Via C. Saldini 50, I-20133 Milano,...

The KP equation with quasiperiodic initial data

The Kadomtsev-Petviashvili (KP) equation is known to admit exact, quasiperiodic solutions that can be written in terms of Riemann theta functions, with a nite number of phases in each solution. In this paper, we propose a method to solve the initial-value problem for the KP equation, for initial data taken from this class of quasiperiodic functions.

On the validity of formal asymptotic expansions in Allen-Cahn equation and FitzHugh-Nagumo system with generic initial data

Formal asymptotic expansions have long been used to study the singularly perturbed Allen-Cahn type equations and reaction-diffusion systems, including in particular the FitzHugh-Nagumo system. Despite their successful role, it has been largely unclear whether or not such expansions really represent the actual profile of solutions with rather general initial data. By combining our earlier result...

Decay Characterization for Solutions to Dissipative Equations in Terms of the Initial Datum

By examining the Fourier transform of the initial datum near the origin, we define the decay character of the datum and provide a method to study the lower and upper algebraic rates of decay of solutions to a wide class of dissipative system of equations.

Approximating Initial-Value Problems with Two-Point Boundary-Value Problems: BBM-Equation