We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be C.

In this paper, a constant speed control of slider-crank mechanisms for machine tools is proposed. A joint-task space hybrid controller based on second-order sliding mode and time-base generator was used to guarantee trajectory tracking complete turn the mechanism crank. switching criterion implemented in order avoid singularities located at two extreme positions slider stroke. trapezoidal profi...

due to some difficulties during seismic data acquisition, like natural obstacles (high voltage electricity cable, bad coupling of geophones with the ground) some of the traces cannot be recorded. since bad traces make the final stack unclear, usually bad traces go mute while processing. the final image of the earth’s crust is highly dependent of the quality and resolution of acquired data and m...

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 = ∫

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...

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 < ∞....

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.