Sentence examples for some parabolic from inspiring English sources
This chapter studies some parabolic and hyperbolic PDEs that contain hysteresis operators.
Finally, Section 4 is devoted to giving important comments and applications of our results on controllability for some parabolic systems.
As far as we know, this seems to be the first paper, where the blow-up phenomenon is studied with variable exponents for the initial and boundary value problem to some parabolic and hyperbolic systems.
While the TPEg content in the dispersed phase is above 30 wt%, the impact fracture surface exhibits drastically enlarged slow crack growth region and some parabolic markings in the fast crack growth region.
Afterwards, the alternating segment algorithms (AGE scheme, ASE-I scheme, and ASC-N scheme) above became very effective methods for some parabolic equations, such as heat equation [7], convection diffusion equation [8 10], dispersive equation [11 16], forth-order parabolic equation [17 19].
Based on Shen's work for the fundamental solution of L in [23], we establish the following upper bound for semigroup kernels Kt x,y), associated to e−tL,0≤Kt x,y)≤Cht(x−y)e−εdμ x,y,t), where ht(x)="(4πt)−n/2e−|x|2/(4t), and dμ x,y,t) is some parabolic type distance function associated with μ.
In the first paper, "On the time periodic free boundary associated to some nonlinear parabolic equations," M. Badii and J. I. Daz prove some qualitative properties of the time periodic free boundary generated by the solution of a general class of second-order quasilinear equations, which, include for example, the -Laplacian operator.
In this paper, we study the blow-up phenomenon for some nonlinear parabolic problems.
Examples in [30] indicate that the blow-up may occur in the interior of the domain for some semilinear parabolic equation if the heat supply through the boundary is fast enough.
Some well-known parabolic equations are the special cases of this equation.
That is, we prove that there exists some skew product parabolic maps that have wandering Fatou disks.
