On wellposedness of the second order accuracy difference scheme for. The wellposedness of difference schemes of the initial value problem for delay differential equations with unbounded operators acting on delay terms in an arbitrary banach space is studied. Wellposed and illposed boundary value problems for pde. In practice, the coercive stability estimates in holder norms for the solutions of difference schemes of the. A parabolic partial differential equation is a type of partial differential equation pde. The study of partial differential equations involving variableexponent nonlinearities has attracted the attention of researchers in recent years. On stability of difference schemes in fractional spacesmathematical and computer. The main purpose of this paper is to establish the wellposedness of this equation in c.
Fractional parabolic differential and difference equations with the. Difference schemes for delay parabolic equations with periodic boundary conditions. The wellposedness of 3 in difference analogues of spaces of smooth functions is established and the coercive stability estimates for the solution of difference schemes for the fractional parabolic equation with nonlocal boundary conditions in a space variable and the 2m th order multidimensional fractional parabolic equation are obtained in. The investigation is based on a new notion of positivity of difference operators in banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Sozencomputersandmathematicswithapplications602010792 802 793 thecoercivityinequalitiesmaximalregularity,wellposedness. On wellposedness of vectorvalued fractional differential difference equations. We are concerned here with wellposed problems for the partial differential. Buy partial differential equations of parabolic type dover books on mathematics on. Theorems on the wellposedness of these difference schemes in fractional spaces are proved. Let a be a strongly positive operator in a banach space e and f t c e then, for the solution u t in c e of the initial value problem 1 the stability inequality holds. Wellposedness of parabolic differential and difference.
A wellknown and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Partial differential equations of parabolic type dover books on. Pdf wellposedness of delay parabolic difference equations. Wellposedness of fractional parabolic equations boundary value. Notice that this equation do not yield a wellposed problem, as it may have several solutions. Wellposedness of parabolic differential and difference equations with the fractional differential operator malaysian journal of mathematical sciences 75 theorem 1.
Wellposedness of nonlocal parabolic differential problems with. In the present paper, we consider the abstract cauchy problem for the fractional differential equation 1 in an arbitrary banach space e with the. Parabolic pdes are used to describe a wide variety of timedependent. On wellposedness of vectorvalued fractional differential. The nonlocal boundary value problem for the parabolic differential equation in an arbitrary banach space with the dependent linear positive operator is. Moreover, applications of operator approach to investigate for stability of difference schemes for fractional parabolic partial differential equations.
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