A characterization of convex calibrable sets in with respect to anisotropic norms
A counterexample in regularity theory for parabolic systems
A criterion of Petrowsky's kind for a degenerate quasilinear parabolic equation.
The celebrated criterion of Petrowsky for the regularity of the latest boundary point, originally formulated for the heat equation, is extended to the so-called p-parabolic equation. A barrier is constructed by the aid of the Barenblatt solution.
A degenerate parabolic equation in noncylindrical domains.
A degenerate parabolic system for three-phase flows in porous media
A classical model for three-phase capillary immiscible flows in a porous medium is considered. Capillarity pressure functions are found, with a corresponding diffusion-capillarity tensor being triangular. The model is reduced to a degenerate quasilinear parabolic system. A global existence theorem is proved under some hypotheses on the model data.
A finite difference scheme for a degenerated diffusion equation arising in microbial ecology.
A free boundary problem describing the saturated-unsaturated flow in a porous medium.
A generalized maximum principle for boundary value problems for degenerate parabolic operators with discontinuous coefficients
We prove a generalized maximum principle for subsolutions of boundary value problems, with mixed type unilateral conditions, associated to a degenerate parabolic second-order operator in divergence form.
A global existence-global nonexistence conjecture of Fujita type for a system of degenerate semilinear parabolic equations
A multiplicity result for a class of quasilinear elliptic and parabolic problems.
A new kind of the solution of degenerate parabolic equation with unbounded convection term
A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
A nonlinear oblique derivative boundary value problem for the heat equation : analogy with the porous medium equation
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...
A notion of renormahzed solution of the study of a general conservation law.
A parabolic analogue of Finn's maximum principle.
A parabolic quasilinear problem for linear growth functionals.
We prove existence and uniqueness of solutions for the Dirichlet problem for quasilinear parabolic equations in divergent form for which the energy functional has linear growth.
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the -norm, independent of the diffusion parameter . The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...
A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations
This paper is devoted to the study of a posteriori error estimates for the scalar nonlinear convection-diffusion-reaction equation . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the L1-norm, independent of the diffusion parameter D. The resulting a posteriori error estimate is used to define an grid adaptive solution algorithm for the finite volume scheme. Finally numerical experiments underline the applicability...
A remark on a Harnack inequality for degenerate parabolic equations
A remark on the uniqueness of fundamental solutions to the -Laplacian equation, .