查看更多>>摘要：This paper is concerned with the Navier-Stokes/Allen-Cahn system,which is used to model the dynamics of immiscible two-phase flows.We consider a 1D free boundary problem and assume that the viscosity coefficient depends on the density in the form ofη(p)=pα.The existence of unique global H2m-solutions(m ∈ N)to the free boundary problem is proven for when 0＜α＜1/4.Furthermore,we obtain the global C∞-solutions if the initial data is smooth.
查看更多>>摘要：Motivated by recent advances made in the study of dividend control and risk management problems involving the U.S.bankruptcy code,in this paper we follow[44]to revisit the De Finetti dividend control problem under the reorganization process and the regulator's intervention documented in U.S.Chapter 11 bankruptcy.We do this by further accommodating the fixed transaction costs on dividends to imitate the real-world procedure of dividend payments.Incorporating the fixed transaction costs transforms the targeting optimal dividend problem into an impulse control problem rather than a singular control problem,and hence computations and proofs that are distinct from[44]are needed.To ac-count for the financial stress that is due to the more subtle concept of Chapter 11 bankruptcy,the surplus process after dividends is driven by a piece-wise spectrally negative Lévy process with endogenous regime switching.Some explicit expressions of the expected net present val-ues under a double barrier dividend strategy,new to the literature,are established in terms of scale functions.With the help of these expressions,we are able to characterize the optimal strategy among the set of admissible double barrier dividend strategies.When the tail of the Lévy measure is log-convex,this optimal double barrier dividend strategy is then verified as the optimal dividend strategy,solving our optimal impulse control problem.
查看更多>>摘要：This paper is devoted to the study of the shape of the free boundary for a three-dimensional axisymmetric incompressible impinging jet.To be more precise,we will show that the free boundary is convex to the fluid,provided that the uneven ground is concave to the fluid.
查看更多>>摘要：In this paper,we study the one-dimensional motion of viscous gas near a vacuum,with the gas connecting to a vacuum state with a jump in density.The interface behavior,the pointwise decay rates of the density function and the expanding rates of the interface are obtained with the viscosity coefficient u(ρ)=ρα for any 0＜α＜1;this includes the time-weighted boundedness from below and above.The smoothness of the solution is discussed.Moreover,we construct a class of self-similar classical solutions which exhibit some interesting properties,such as optimal estimates.The present paper extends the results in[Luo T,Xin Z P,Yang T.SIAM J Math Anal,2000,31(6):1175-1191]to the jump boundary conditions case with density-dependent viscosity.
查看更多>>摘要：Let X={X(t)∈ Rd,t ∈ RN} be a centered space-time anisotropic Gaussian field with indices H=(H1,…,HN)∈(0,1)N,where the components Xi(i=1,…,d)of X are independent,and the canonical metric √E(Xi(t)-Xi(s))2(i=1,…,d)is commensurate with γαi(ΣNj=1|tj-sj|Hj)for s=(s1,…,sN),t=(t1,…,tN)∈ RN,αi ∈(0,1],and with the continuous function γ(·)satisfying certain conditions.First,the upper and lower bounds of the hitting probabilities of X can be derived from the corresponding generalized Hausdorff measure and capacity,which are based on the kernel functions depending explicitly on γ(·).Furthermore,the multiple intersections of the sample paths of two independent centered space-time anisotropic Gaussian fields with different distributions are considered.Our results extend the corresponding results for anisotropic Gaussian fields to a large class of space-time anisotropic Gaussian fields.
查看更多>>摘要：In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the form L(f)=zfz-(-z)f(-z),where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of Bloch-Landau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.
查看更多>>摘要：In this paper,we define a new class of control functions through aggregate special functions.These class of control functions help us to stabilize and approximate a tri-additiveψ-functional inequality to get a better estimation for permuting tri-homomorphisms and permuting tri-derivations in unital C*-algebras and Banach algebras by the vector-valued alternative fixed point theorem.
查看更多>>摘要：We consider the interior transmission eigenvalue problem corresponding to the scattering for an anisotropic medium of the scalar Helmholtz equation in the case where the boundary ∂Ω is split into two disjoint parts and possesses different transmission condition-s.Using the variational method,we obtain the well posedness of the interior transmission problem,which plays an important role in the proof of the discreteness of eigenvalues.Then we achieve the existence of an infinite discrete set of transmission eigenvalues provided that n ≡ 1,where a fourth order differential operator is applied.In the case of n(≡)1,we show the discreteness of the transmission eigenvalues under restrictive assumptions by the analytic Fredholm theory and the T-coercive method.
查看更多>>摘要：In this paper,we consider entire solutions of higher order homogeneous differen-tial equations with the entire coefficients having the same order,and prove that the entire solutions are of infinite lower order.The properties on the radial distribution,the limit di-rection of the Julia set and the existence of a Baker wandering domain of the entire solutions are also discussed.
查看更多>>摘要：Clifford analysis is an important branch of modern analysis;it has a very im-portant theoretical significance and application value,and its conclusions can be applied to the Maxwell equation,Yang-Mill field theory,quantum mechanics and value problems.In this paper,we first give the definition of a quasi-Cauchy type integral in complex Clifford analysis,and get the Plemelj formula for it.Second,we discuss the Holder continuity for the Cauchy-type integral operators with values in a complex Clifford algebra.Finally,we prove the existence of solutions for a class of linear boundary value problems and give the integral representation for the solution.
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