Blowup Rate Estimate for a System of Semilinear Parabolic Equations

Blowup Analysis for a Semilinear Parabolic System with Nonlocal Boundary Condition

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...

VARIATIONAL DISCRETIZATION AND MIXED METHODS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS WITH INTEGRAL CONSTRAINT

The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L2 are established for the state...

Solving the inverse problem of determining an unknown control parameter in a semilinear parabolic equation

The inverse problem of identifying an unknown source control param- eter in a semilinear parabolic equation under an integral overdetermina- tion condition is considered. The series pattern solution of the proposed problem is obtained by using the weighted homotopy analysis method (WHAM). A description of the method for solving the problem and nding the unknown parameter is derived. Finally, tw...

On blowup for semilinear wave equations with a focusing nonlinearity

In this paper we report on numerical studies of formation of singularities for the semilinear wave equations with a focusing power nonlinearity utt−∆u = u in three space dimensions. We show that for generic large initial data that lead to singularities, the spatial pattern of blowup can be described in terms of linearized perturbations about the fundamental selfsimilar (homogeneous in space) so...