[PDF] Top 20 Remarks on weak solutions for a nonlocal parabolic problem

... the nonlocal term a we cannot, in the present problem, make a direct adaptation of the classical ...of weak solution for problem ...periodic weak solution for problem ... See full document

... In this paper, we not only give the asymptotic behavior at the origin for the maximum modulus of weak solutions of the stationary Schrödinger equation in a cone but also obtain the prope[r] ... See full document

... [5] A. El Hachimi and M. R. Sidi Ammi, Existence of weak solutions for the thermistor problem with degeneracy, Proceedings of the 2002 Fez Conference on Partial Differential Equations, Electron. J. ... See full document

... mixed problem with nonlocal boundary conditions, for the quasilinear parabolic ...the weak generalized solution, and also continuous dependence upon the data of the solution are shown by using ... See full document

... The outline of this paper is as follows. In Section 2, we introduce the function spaces of Orlicz-Sobolev type, give the definition of a weak solution to the problem, and prove the existence and uniqueness. ... See full document

... seen, problem (P) includes parabolic equation which is nonlinear with re- spect to the gradient of the solution, and with variable exponents of ...solve problem (P) under the framework of Sobolev ... See full document

... Inspired by the note mentioned above by Marino and Maugeri, in the present note, the authors extend differentiability properties to the case of parabolic systems of order 2m. More precisely, let Ω be an open ... See full document

... and parabolic problems are already present in simple models as those we shall analyse in this ...with nonlocal terms the issue of positivity is far from trivial and may require a detailed study via the ... See full document

... In this is work he proved the existence of classical solution by iterative methods for the mixed problem associated to the equation... EXISTENCE OF WEAK SOLUTIONS FOR CAUCHY PROBLEMS.[r] ... See full document

... exact solutions, along with the relative errors at some nodal points in Tables 5-6 and 7-8, ...exact solutions and the accuracy of approximate solution is getting better as n ...approximate solutions ... See full document

... The problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theo- ... See full document

... classical solutions for the regularized problem corresponding to the Dirichlet boundary problem ...the solutions for the degenerate problem ... See full document

... This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and global existence ... See full document

... of weak solutions of parabolic equation with p-growth conditions, where p is a constant, for example 8, ...the weak solutions plays a central role in many ... See full document

... real-valued function, M is a continuous function which obey some specific conditions. The purpose of the present paper is to find a nontrivial weak solution for a p (x)-Kirchhoff-type equation (P) in the variable ... See full document

... To our knowledge, there is no work dealing with the parabolic system 1.1 with nonlocal boundary condition 1.2 except for the single equation case, although this is a very classical model. Therefore, the ... See full document

... of weak or strong solutions and regularity properties of classical Navier-Stokes problems were extensively studied, ...value problem for the Navier-Stokes equation ( see, ...global weak ... See full document

... Observe that on the set K x, t 0 the equation 1 7 degenerate into parabolic equation In this paper we study existence and uniqueness of weak solution of the mixed problem for the equatio[r] ... See full document

... The nonlocal problems have been intensively studied using various frames and tech- niques, and they continue to be an important research ...mild solutions for nonlocal (autonomous or nonau- tonomous) ... See full document

... To our surprise, however, it seems that there is no work dealing with singularity analysis of the parabolic system 1.1 with nonlocal boundary condition 1.2 except for the single equation case, although this ... See full document