This paper is concerned with the asymptotic stability of solution to an initial-boundary value problem on half line for a hyperbolic-elliptic coupled system radiating gas, where data boundary and at far field state are defined as $u_-$ $u_+$ satisfying $u_-<u_+$. For scalar viscous conservation law case, it known by work Liu, Matsumura, Nishihara [SIAM J. Math. Anal., 29 (1998), pp. 293--308] t...

In this paper, a strongly nonlinear coupled elliptic-parabolic system modelling a class of engineering problems with heat effect is studied. Existence of a weak solution is first established by Schauder fixed point theorem, where the coupled functions σ(s), k(s) are assumed to be bounded. The uniqueness of the solution is obtained by applying Meyers’ theorem and assuming that σ(s), k(s) are Lip...

The Bidomain model describes the spread of electrical excitation in the anisotropic cardiac tissue in terms of the evolution of the transmembrane and extracellular electric potentials, v and ue respectively. This model consists of a non-linear parabolic reaction-diffusion partial differential equation (PDE) for v, coupled with an elliptic linear PDE for ue. The evolution equation is coupled thr...

An SPICE compatible model for multiple coupled nonuniform lossless transmission lines (TL's) is presented. The method of the modeling is based on the steplines approximation of the nonuniform TLs and quasi-TEM assumptions. Using steplines approximation the system of coupled nonuniform TLs is subdivided into arbitrary large number of coupled uniform lines (steplines) with different characteristi...

We study the existence of classical solutions to a broad class local, first order, forward-backward extended mean field games systems, that includes standard games, with congestion, and type control problems. work strictly monotone cost may be fully coupled Hamiltonian, which is assumed have superlinear growth. Following previous on order system, we prove smooth under coercivity condition ensur...

‎By the Mordell‎- ‎Weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎This paper studies the rank of the family Epq:y2=x3-pqx of elliptic curves‎, ‎where p and q are distinct primes‎. ‎We give infinite families of elliptic curves of the form y2=x3-pqx with rank two‎, ‎three and four‎, ‎assuming a conjecture of Schinzel ...

Numerical methods for elliptic partial differential equations (PDEs) within both continuous (CG) and hybridized discontinuous Galerkin (HDG) frameworks share the same general structure: local (elemental) matrix generation followed by a global linear system assembly and solve. The lack of inter-element communication and easily parallelizable nature of the local matrix generation stage coupled wi...