In this paper, the modified Korteweg-de Vries (mKdV) equation with variable coefficients (vc-mKdV equation) is investigated via two kinds of approaches and symbolic computation. On the one hand, we firstly reduce the vc-mKdV equation to a second-order nonlinear nonhomogeneous ODE using travelling wave-like similarity transformation. And then we obtain its many types of exact fractional solution...

We develop and analyze multilevel methods for nonuniformly elliptic operators whose ellipticity holds in a weighted Sobolev space with an A2–Muckenhoupt weight. Using the so-called Xu–Zikatanov (XZ) identity, we derive a nearly uniform convergence result, under the assumption that the underlying mesh is quasi-uniform. We also consider the so-called α-harmonic extension to localize fractional po...

Abstract Aiming at the problems of image edge blur and detail loss in most denoising models, an model based on improved fractional calculus is proposed. Through classification noise, integer order PDE discussed. Based mathematical theory calculus, The by combining texture detection operator, gray value smoothing factor fast algorithm. simulation experiment carried out MATLAB platform. results s...

Abstract The BBM equation is a Hamiltonian PDE which revealed to be very interesting test-model study the transformation property of Gaussian measures along flow, after Tzvetkov (Sigma 3:e28-35). In this paper we with critical dispersion (which Benjamin-Ono type model). We prove that image supported on fractional Sobolev spaces increasing regularity are absolutely continuous, but cannot identif...

background: the increasing use of nuclear radiation for human welfare necessitates the search for new, safe, cost effective radio protectors not only for the personnel’s charged with the responsibility of working or testing with radiations in laboratories, but also for general public. with this view the present study has been undertaken to determine the deleterious effects of sub lethal gamma r...

Although there are many methods for image denoising, but partial differential equation (PDE) based denoising attracted much attention in the field of medical image processing such as magnetic resonance imaging (MRI). The main advantage of PDE-based denoising approach is laid in its ability to smooth image in a nonlinear way, which effectively removes the noise, as well as preserving edge throug...

BACKGROUND The NO--cGMP system plays a key role in the regulation of sinusoidal tonus and liver blood flow with phosphodiesterase-5 (PDE-5) terminating the dilatory action of cGMP. We, therefore, investigated the effects of PDE-5 inhibitors on hepatic and systemic hemodynamics in rats. METHODS Hemodynamic parameters were monitored for 60 min. after intravenous injection of sildenafil and vard...

This note is devoted to stabilizing a coupled PDE–ODE system with interaction at the interface. First, a state feedback boundary controller is designed, and the system is transformed into an exponentially stable PDE–ODE cascadewith an invertible integral transformation,where PDE backstepping is employed. Moreover, the solution to the resulting closed-loop system is derived explicitly. Second, a...

By now it is clear that computational science is one of the bases, together with theory and experiments, of scientific inquiry. A carefully crafted computational model/experiment can replace a very expensive or unrealizable experimental setting, and it can give new insight into the theoretical developments of a specific discipline. Discussions about computer aided simulation and high performanc...