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We study a class of ultra-parabolic equations, it is a high order degenerate parabolic operators of Hormander type, so it is strongly degenerate, but we prove that this class operators possesses the a...
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Quasi-linear perturbations of a two-dimensional flow with a first integral and the corresponding parabolic PDE’s with a small parameter at the second order derivatives are considered in th...
In this paper, we investigate the quenching phenomena of initial boundary value problem for the fourth-order nonlinear parabolic equations in bounded domains. First, we not only obtain quenching pheno...
In this paper, we investigate the quenching phenomena of the Cauchy problem for the second-order nonlinear parabolic equation on unbounded domain. It is shown that the solution quenches in finite time...
In this paper, we study the boundary value problem of the classical semilinear parabolic equations ut − u = |u|p−1u.
We prove two assumptions made in an article by Ya.A. Butko, M. Grothaus,O.G. Smolyanov concerning the existence of a strongly continuous operator semi-group solving a Cauchy-Dirichlet problem for an e...
The heat-bal ance in te gral method of Good man has been thor oughly an a lyzed in the case of a par a bolic pro file with un spec i fied ex po nent de pend ing on the bound ary con di tion im posed. ...
The heat-bal ance in te gral method of Good man is stud ied with two sim ple 1-D heat con duc tion prob lems with pre scribed tem per a ture and flux bound ary con di tions.These clas si cal prob lems...
The parabolic Anderson problem with a random potential obtained by attaching a long tailed potential around a randomly perturbed lattice is studied.The moment asymptotics of the total mass of the solu...
Associated to a composition of M and a composition of N, a new presentation of the super Yangian of the general linear Lie superalgebra Y (glM|N) is obtained.
The first part of the paper discusses a second-order quasilinear parabolic equation in a vector bundle over a compact manifold M with boundary @M. We establish a short-time existence theorem for this ...
In this paper, we study k-parabolic arrangements, a generalization of the k-equal arrangement for any nite real re ection group. When k =2, these arrangements correspond to the well-studied Coxeter a...
In [BR1], [BR2], a parabolic determinant line bundle on a moduli space of stable parabolic bundles was constructed, along with a Hermitian structure on it.The construction of the Hermitian structure w...
We consider a discrete-time version of the parabolic Anderson model. This may be described as a model for a directed (1+ d)-dimensional polymer interacting with a random potential, which is constant i...

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