Observations on quasi-linear partial differential equations
On a Caginalp phase-field system with a logarithmic nonlinearity
We consider a phase field system based on the Maxwell Cattaneo heat conduction law, with a logarithmic nonlinearity, associated with Dirichlet boundary conditions. In particular, we prove, in one and two space dimensions, the existence of a solution which is strictly separated from the singularities of the nonlinear term and that the problem possesses a finite-dimensional global attractor in terms of exponential attractors.
On a class of initial-boundary value problems in a domain with boundary containing isolated points
On a class of multitime evolution equations with nonlocal initial conditions.
On a Class of non Linear Schrödinger Equations with non Local Interaction.
On a Class of Retarded Partial Differential Equations.
On a Class of Time Inhomogeneous Nonsingular Flows and Schrödinger Operators.
On a Class of Unilateral Evolution Problems.
On a conserved Penrose-Fife type system
We deal with a class of Penrose-Fife type phase field models for phase transitions, where the phase dynamics is ruled by a Cahn-Hilliard type equation. Suitable assumptions on the behaviour of the heat flux as the absolute temperature tends to zero and to are considered. An existence result is obtained by a double approximation procedure and compactness methods. Moreover, uniqueness and regularity results are proved as well.
On a critical threshold for nonlinear diffusion equations.
We study some aspects of the asymptotic behavior of the solutions to a class of nonlinear parabolic equations.
On a fourth order equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Fourth Order Equation in 3-D
In this article we study the positivity of the 4-th order Paneitz operator for closed 3-manifolds. We prove that the connected sum of two such 3-manifold retains the same positivity property. We also solve the analogue of the Yamabe equation for such a manifold.
On a Free Boundary Problem for a Nonlinear Coupled System of Evolution Equations of Oceanography.
On a generalized nonlinear equation of Schrödinger type.
On a holomorphic solution of a singular partial differential equation with many simple poles
On a mixed problem for a constant coefficient second-order system.
On a nonlinear degenerate evolution equation with strong damping.
On a parabolic-hyperbolic Penrose-Fife phase-field system.
On a regularizing effect of Schrödinger type groups
On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments
We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.