Well-posedness and Regularity for Quasilinear Degenerate Parabolic-hyperbolic Spde
نویسنده
چکیده
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results based on averaging techniques. Second, we prove the existence and uniqueness of solutions in a full L1 setting requiring no growth assumptions on the nonlinearities. In addition, we prove a comparison result and an L1-contraction property for the solutions.
منابع مشابه
A Regularity Result for Quasilinear Stochastic Partial Differential Equations of Parabolic Type
We consider a non degenerate quasilinear parabolic stochastic partial differential equation with a uniformly elliptic diffusion matrix. It is driven by a nonlinear noise. We study regularity properties of its weak solution satisfying classical a priori estimates. In particular, we determine conditions on coefficients and initial data under which the weak solution is Hölder continuous in time an...
متن کاملDegenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L1-contraction property. In comparison to the previous works of the authors concerning stochastic...
متن کاملWell-posedness of a quasilinear hyperbolic fluid model
We replace a Fourier type law by a Cattaneo type law in the derivation of the fundamental equations of fluid mechanics. This leads to hyperbolicly perturbed quasilinear Navier-Stokes equations. For this problem the standard approach by means of quasilinear symmetric hyperbolic systems seems to fail by the fact that finite propagation speed might not be expected. Therefore a somewhat different a...
متن کامل? W H A T I S . . . a Kinetic Solution for Degenerate Parabolic - Hyperbolic Equations ?
Nonlinear degenerate parabolic-hyperbolic equations are one of the most important classes of nonlinear partial differential equations. Nonlinearity and degeneracy are two main features of these equations and yield several striking phenomena that require new mathematical ideas, approaches, and theories. On the other hand, because of the importance of these equations in applications, there is a l...
متن کاملWell-posedness of a quasilinear hyperbolic-parabolic system arising in mathematical biology∗
We study the existence of classical solutions of a taxis-diffusion-reaction model for tumour-induced blood vessel growth. The model in its basic form has been proposed by Chaplain and Stuart (IMA J. Appl. Med. Biol. (10), 1993) and consists of one equation for the endothelial cell-density and another one for the concentration of tumour angiogenesis factor (TAF). Here we consider the special and...
متن کامل