相关论文: On some properties of entropy solutions of degener…

We prove existence of the largest entropy sub-solution and the smallest entropy super-solution to the Cauchy problem for a nonlinear degenerate parabolic equation with only continuous flux and diffusion functions. Applying this result, we…

Under a precise nonlinearity-diffusivity assumption we establish the decay of entropy solutions of a degenerate nonlinear parabolic equation with initial data being a sum of periodic function and a function vanishing at infinity (in the…

Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.

We are interested in the large-time behavior of periodic entropy solutions in $L^\infty$ to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer…

We discuss the well-posedness and decay of Besicovitch almost periodic solutions for a class of nonlinear degenerate anisotropic hyperbolic-parabolic equations. In our definition of weak entropy solution the initial data is only assumed in…

We consider the Cauchy problem for a class of nonlinear degenerate parabolic equa- tion with forcing. By using the vanishing viscosity method we obtain generalized solutions. We prove some regularity results about this generalized…

We find an explicit form of entropy solutions to a Riemann problem for a degenerate nonlinear parabolic equation with piecewise constant velocity and diffusion coefficients. It is demonstrated that this solution corresponds to the minimum…

We consider the Cauchy problem for a stochastic scalar parabolic-hyperbolic equation in any space dimension with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional…

We consider the Cauchy problem for doubly non-linear degenerate parabolic equations on Riemannian manifolds of infinite volume, or in $\R^N$. The equation contains a weight function as a capacitary coefficient which we assume to decay at…

We prove the asymptotic convergence of a space-periodic entropy solution of a one-dimensional degenerate parabolic equation to a traveling wave. It is also shown that on a segment containing the essential range of the limit profile the flux…

Under a precise genuine nonlinearity assumption we establish the decay of entropy solutions of a multidimensional scalar conservation law with merely continuous flux and with initial data being a sum of periodic function and a function…

This paper studies the properties of solutions for a double nonlinear time-dependent parabolic equation with variable density, not in divergence form with a source or absorption. The problem is formulated as a partial differential equation…

We study the Cauchy problem for a scalar semilinear degenerate parabolic partial differential equation with stochastic forcing. In particular, we are concerned with the well-posedness in any space dimension. We adapt the notion of kinetic…

Here, we consider anisotropic degenerate parabolic-hyperbolic equations and degenerate quasilinear Hamilton-Jacobi equations. We prove the equivalence of two notions of entropy and viscosity solutions of two equations, and apply it to…

We introduce the notion of entropy solutions (e.s.) to a conservation law with an arbitrary jump continuous flux vector and prove existence of the largest and the smallest e.s. to the Cauchy problem. The monotonicity and stability…

We prove the well-posedness and the asymptotic decay to the mean value of Besicovitch almost periodic entropy solutions to nonlinear aniso\-tropic degenerate parabolic-hyperbolic equations. After setting up the problem and its kinetic…

We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-time regularity under a non-degeneracy condition that does…

In this paper, the method of constructing the asymptotics of the fundamental solution of the Cauchy problem for a degenerate linear parabolic equation with small diffusion is considered. Based on the results obtained in \cite{dn}, the study…

In this paper, we develop a universal, conceptually simple and systematic method to prove well-posedness to Cauchy problems for weak solutions of parabolic equations with non-smooth, time-dependent, elliptic part having a variational…

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…