Semilinear parabolic partial differential equations—theory, approximation, and application
نویسنده
چکیده
We present an abstract framework for semilinear parabolic problems based on analytic semigroup theory. The same framework is used for numerical discretization based on the finite element method. We prove local existence of solutions and local error estimates. These are applied in the context of dynamical systems. The framework is also used to analyze the finite element method for a stochastic parabolic equation.
منابع مشابه
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...
متن کاملAPPROXIMATION OF STOCHASTIC PARABOLIC DIFFERENTIAL EQUATIONS WITH TWO DIFFERENT FINITE DIFFERENCE SCHEMES
We focus on the use of two stable and accurate explicit finite difference schemes in order to approximate the solution of stochastic partial differential equations of It¨o type, in particular, parabolic equations. The main properties of these deterministic difference methods, i.e., convergence, consistency, and stability, are separately developed for the stochastic cases.
متن کاملOn the Galerkin method for semilinear parabolic-ordinary systems
We consider a general system of n1 semilinear parabolic partial differential equations and n2 ordinary differential equations, with locally Lipschitz continuous nonlinearities. We analyse the well-posedness of this problem, exploiting the tools of the semigroups theory, and derive other further regularity results and conditions for the boundedness of the solution. We define the Galerkin semidis...
متن کاملA High Order Finite Dierence Method for Random Parabolic Partial Dierential Equations
In this paper, for the numerical approximation of random partial differential equations (RPDEs) of parabolic type, an explicit higher order finite difference scheme is constructed. In continuation the main properties of deterministic difference schemes, i.e. consistency, stability and convergency are developed for the random cases. It is shown that the proposed random difference scheme has thes...
متن کاملExistence and Uniqueness to the Cauchy Problem for Linear and Semilinear Parabolic Equations with Local Conditions
We consider the Cauchy problem in R for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The line...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006