Regularity Results for the Minimum Time Function of a Class of Semilinear Evolution Equations of Parabolic Type

An inverse problem of identifying the coefficient of semilinear parabolic equation

    In this paper, a variational iteration method (VIM), which is a well-known method for solving nonlinear equations, has been employed to solve an inverse parabolic partial differential equation. Inverse problems in partial differential equations can be used to model many real problems in engineering and other physical sciences. The VIM is to construct correction functional using general Lagr...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Regularity results for a class of Semilinear Parabolic Degenerate Equations and Applications

We prove some regularity results for viscosity solutions to strongly degenerate parabolic semilinear problems. These results apply to a specific model used for pricing Mortgage-Backed Securities and allow a complete justification of use of the classical Ito’s formula. AMS subject classifications: 35K55, 35K65 , 35B65, 60H30, 91B70.

Notes on Global Attractors for a Class of Semilinear Degenerate Parabolic Equations

We study the regularity and fractal dimension estimates of global attractors for a class of semilinear degenerate parabolic equations in bounded domains.

Hamiltonian Pontryagin’s Principles for Control Problems Governed by Semilinear Parabolic Equations

In this paper we study optimal control problems governed by semilinear parabolic equations. We obtain necessary optimality conditions in the form of an exact Pontryagin’s minimum principle for distributed and boundary controls (which can be unbounded) and bounded initial controls. These optimality conditions are obtained thanks to new regularity results for linear and nonlinear parabolic equati...