The paper deals with the existence of solutions of some parabolic bilateral problems approximated by the renormalized solutions of some parabolic equations.

We consider a class of higher order nonlinear degenerate parabolic systems, whose easiest model is the parabolic p-Laplacean system ∫ ΩT ( u · φt − |Dmu|p−2Dmu ·Dmφ ) dz = ∫

It is well known that the parabolic partial differential equations in two or more space dimensions with overspecified boundary data, feature in the mathematical modeling of many phenomena. In this article, an inverse problem of determining an unknown time-dependent source term of a parabolic equation in general dimensions is considered. Employing some transformations, we change the inverse prob...

In this paper we consider the nonlinear parabolic integro-differential equation with initial and boundary conditions. We develop the method of generalized quasilinearization to generate linear iterates that converge quadratically to the unique solution of the nonlinear parabolic integro-differential equation. For this purpose, we establish comparison results for the parabolic integro-differenti...

In this paper we study variational problems related to the heat equation in metric spaces equipped with a doubling measure and supporting a Poincaré inequality. We give a definition of parabolic De Giorgi classes and compare this notion with that of parabolic quasiminimizers. The main result, after proving the local boundedness, is the proof of a scale-invariant Harnack inequality for functions...

Let (G,E) be a graph with weights {axy} for which a parabolic Harnack inequality holds with space-time scaling exponent β ≥ 2. Suppose {axy} is another set of weights that are comparable to {axy}. We prove that this parabolic Harnack inequality also holds for (G,E) with the weights {axy}. We also give stable necessary and sufficient conditions for this parabolic Harnack inequality to hold.

Roger W. Richardson proved that any parabolic subgroup of a complex semisimple Lie group admits an open dense orbit in the nilradical of its corresponding parabolic subalgebra. In the case of complex symmetric spaces we show that there exist some large classes of parabolic subgroups for which the analogous statement which fails in general, is true. Our main contribution is the extension of a th...

In this paper, we show a parabolic version of the Ogawa type inequality in Sobolev spaces. Our inequality provides an estimate of the L∞ norm of a function in terms of its parabolic BMO norm, with the aid of the square root of the logarithmic dependency of a higher order Sobolev norm. The proof is mainly based on the Littlewood-Paley decomposition and a characterization of parabolic BMO spaces....

In this paper, we study the semi-discrete Galerkin finite element method for parabolic equations with Lipschitz continuous coefficients. We prove the maximumnorm stability of the semigroup generated by the corresponding elliptic finite element operator, and prove the space-time stability of the parabolic projection onto the finite element space in L∞(QT ) and L p((0, T ); Lq ( )), 1 < p, q < ∞....

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...