相关论文: On the Solvability of a Class of Degenerate or Sin…

In this manuscript we establish local H\"older regularity estimates for bounded solutions of a certain class of doubly degenerate evolution PDEs. By making use of intrinsic scaling techniques and geometric tangential methods, we derive…

We introduce elliptic and parabolic $\mathcal{B}_{1}$ classes that generalize the well-known $\mathfrak{B}_{p}$ classes of DeGiorgi, Ladyzhenskaya and Ural'tseva with $p>1$. New classes are applied to prove pointwise continuity of solutions…

We obtain solutions of the nonlinear degenerate parabolic equation \[ \frac{\partial \rho}{\partial t} = {div} \Big\{\rho \nabla c^\star [ \nabla (F^\prime(\rho)+V) ] \Big\} \] as a steepest descent of an energy with respect to a convex…

In this work, we analytically investigate a degenerating PDE system for phase separation and complete damage processes considered on a nonsmooth time-dependent domain with mixed boundary conditions. The evolution of the system is described…

The paper is a comprehensive study of the $L_p$ and the Schauder estimates for higher-order divergence type parabolic systems with discontinuous coefficients in the half space and cylindrical domains with conormal derivative boundary…

We study the local H\"older continuity and the asymptotic behaviour of solution, $\mathbf{u}=(u^1,\cdots, u^k)$, of the degenerate system \begin{equation*} u^i_t=\nabla\cdot\left(m\,U^{m-1}\nabla u^i\right) \qquad \text{for $m>1$ and…

We establish a Gagliardo-Nirenberg-type inequality in $\mathbb{R}^n$ for functions which decay fast as $|x|\to\infty$. We use this inequality to derive upper bounds for the decay rates of solutions of a degenerate parabolic equation.…

We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…

In this paper, we study the global H\"older regularity of solutions to uniformly degenerate parabolic equations. We also study the convergence of solutions as time goes to infinity under extra assumptions on the characteristic exponents of…

We consider the hyperbolic-parabolic singular perturbation problem for a nondegenerate quasilinear equation of Kirchhoff type with weak dissipation. This means that the dissipative term is multiplied by a coefficient b(t) which tends to 0…

In this paper, we study the degenerate or singular fully nonlinear dead-core systems coupled with strong absorption terms. We establish several properties, including improved regularity of viscosity solutions along the free boundary,…

Classical (maximal) superintegrable systems in $n$ dimensions are Hamiltonian systems with $2n-1$ independent constants of the motion, globally defined, the maximum number possible. They are very special because they can be solved…

We consider the problem of existence and uniqueness of strong a.e. solutions $u: \mathbb{R}^n \longrightarrow \mathbb{R}^N$ to the fully nonlinear PDE system \[\label{1} \tag{1} F(\cdot,D^2u ) \,=\, f, \ \ \text{ a.e. on }\mathbb{R}^n, \]…

We prove global existence of nonnegative weak solutions for a strongly coupled, fourth order degenerate parabolic system governing the motion of two thin fluid layers in a porous medium when capillarity is the sole driving mechanism.

In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…

This article studies the partial H\"older continuity of weak solutions to certain degenerate parabolic systems whose model is the differentiable parabolic $p(x,t)$-Laplacian system, \begin{equation*}\partial_t…

Motivated by applications to proving regularity of solutions to degenerate parabolic equations arising in population genetics, we study existence, uniqueness and the strong Markov property of weak solutions to a class of degenerate…

We consider the hyperbolic-parabolic singular perturbation problem for a degenerate quasilinear Kirchhoff equation with weak dissipation. This means that the coefficient of the dissipative term tends to zero when t tends to +infinity. We…

We establish existence and uniqueness for a wide class of Markovian systems of backward stochastic differential equations (BSDE) with quadratic nonlinearities. This class is characterized by an abstract structural assumption on the…

The large-time asymptotics of the solutions to a class of degenerate parabolic cross-diffusion systems is analyzed. The equations model the interaction of an arbitrary number of population species in a bounded domain with no-flux boundary…