相关论文: Parabolic equations with continuous initial data

We develop a quantitative theory of stochastic homogenization for linear, uniformly parabolic equations with coefficients depending on space and time. Inspired by recent works in the elliptic setting, our analysis is focused on certain…

This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general linear parabolic equation of the second order with variable…

In this paper, we will use the maximum principle to give a new proof of the gradient estimates for mean curvature equations with some oblique derivative problems. Specially, we shall give a new proof for the capillary problem with zero…

We present a stochastic numerical method for solving fully non-linear free boundary problems of parabolic type and provide a rate of convergence under reasonable conditions on the non-linearity.

We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.

We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…

This paper is concerned with global estimates and regularity of solutions for the initial value problem of the retarded parabolic equation $$\frac{\patial u}{\patial t}-\Delta u=f(x,u)+g(u(x,t-r_1(t)),\cdots,u(x,t-r_m(t)))+h(x,t)$$ in a…

Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, there was a lack of understanding of parabolic problems with…

We prove new existence and uniqueness results for weak solutions to non-homogeneous initial-boundary value problems for parabolic equations modeled on the evolution of the p-Laplacian.

We consider the homogeneous Dirichlet problem for the anisotropic parabolic equation \[ u_t-\sum_{i=1}^ND_{x_i}\left(|D_{x_i}u|^{p_i(x,t)-2}D_{x_i}u\right)=f(x,t) \] in the cylinder $\Omega\times (0,T)$, where $\Omega\subset \mathbb{R}^N$,…

We consider a degenerate hyperbolic equation of Kirchhoff type with a small parameter epsilon in front of the second-order time-derivative. In a recent paper, under a suitable assumption on initial data, we proved decay-error estimates for…

In this work the evolution of a fluid droplet in vacuum is considered. This means that the surface tension and the fluid forces are in equilibrium at the free boundary. The fluid is governed by the incompressible quasi-steady Stokes…

We construct the fundamental solution of second order parabolic equations in non-divergence form under the assumption that the coefficients are of Dini mean oscillation in the spatial variables. We also prove that the fundamental solution…

In this paper we prove existence and uniqueness results for nonlinear parabolic problems with Dirichlet boundary values whose model is \[ \left\{ \begin{aligned} &b(u)_t-\Delta_{p}u=\mu\;\mbox{in }(0,T)\times\Omega,\\…

In this paper, we establish the existence of a 1-parameter family of spatially inhomogeneous radially symmetric classical self-similar solutions to a Cauchy problem for a semi-linear parabolic PDE with non-Lipschitz nonlinearity and trivial…

In this paper we apply a scaling invariance analysis to reduce a class of parabolic moving boundary problems to free boundary problems governed by ordinary differential equations. As well known free boundary problems are always non-linear…

We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely geometric motion in terms of the wetting domain and the…

The paper considers parabolic equations in non-divergent form with discontinuous coefficients at higher derivatives. Their investigation is most complicated because, in general, in the case of discontinuous coefficients, the uniqueness of a…

This paper studies global a priori gradient estimates for divergence-type equations patterned over the $p$-Laplacian with first-order terms having polynomial growth with respect to the gradient, under suitable integrability assumptions on…

Results of investigation of the asymptotic behavior of solutions to the Cauchy problems for a quasi-linear parabolic equation with a small parameter at a higher derivative near singular points of limit solutions are presented. Interest to…