Nonlinear Elliptic Systems and Nonlinear Parabolic Systems
نویسندگان
چکیده
منابع مشابه
POD Galerkin Schemes for Nonlinear Elliptic-Parabolic Systems
In this paper the authors study a nonlinear elliptic-parabolic system, which is motivated by mathematical models for lithium ion batteries. For the reliable and fast numerical solution of the system a reduced-order approach based on proper orthogonal decomposition (POD) is applied. The strategy is justified by an a-priori error estimate for the error between the solution to the coupled system a...
متن کاملLorentz Spaces and Nonlinear Elliptic Systems
In this paper we study the following system of semilinear elliptic equations: −∆u = g(v) , in Ω, −∆v = f(u) , in Ω, u = 0 and v = 0 , on ∂Ω, where Ω is a bounded domain in R , and f, g ∈ C(R) are superlinear nonlinearities. The natural framework for such systems are Sobolev spaces, which give in most cases an adequate answer concerning the ”maximal growth” on f and g such that the proble...
متن کاملNonlinear Elliptic Systems and Mean Field Games ∗
We consider a class of quasilinear elliptic systems of PDEs consisting of N HamiltonJacobi-Bellman equations coupled with N divergence form equations, generalising to N > 1 populations the PDEs for stationary Mean-Field Games first proposed by Lasry and Lions. We provide a wide range of sufficient conditions for the existence of solutions to these systems: either the Hamiltonians are required t...
متن کاملCompactness Methods for Doubly Nonlinear Parabolic Systems
We study solutions of the system of PDE Dψ(vt) = DivDF (Dv), where ψ and F are convex functions. This type of system arises in various physical models for phase transitions. We establish compactness properties of solutions that allow us to verify partial regularity when F is quadratic and characterize the large time limits of weak solutions. Special consideration is also given to systems that a...
متن کاملNonlinear Transmission Problems for Quasilinear Parabolic Systems
We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Applied Mathematics
سال: 2014
ISSN: 1110-757X,1687-0042
DOI: 10.1155/2014/405123