摘要:

AbstractA boundary‐value problem for a non‐linear second‐order equation of mixed type in a cylindrical domain is considered. This problem simulates the development of small disturbances in a transonic flow of a chemical mixture in a Laval nozzle.The existence of a regular solution is proved with the help ofa prioriestimates for a corresponding linear problem and the contractive mapping theorem. The solution of the linear problem is constructed by the Galerkin m

ISSN:0170-4214    

DOI:10.1002/mma.1670110501

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIt is shown that finite energy states of a vibrating viscoelastic plate of the Kelvin–Voigt type are, in general, not exactly controllable byL2‐boundary controls. Accordingly, we present a result on approximative controllability. The method is gene

ISSN:0170-4214    

DOI:10.1002/mma.1670110502

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractUnder biologically reasonable assumptions the threshold phenomena for the first initial boundary value problem of FitzHugh–Nagumo equations is prove

ISSN:0170-4214    

DOI:10.1002/mma.1670110503

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractThe model equations of the catalytic fixed‐bed reactor often possess solutions in the form of travelling wave fronts similar to the well‐known case of Fisher's equation. The mathematical investigation of these waves requires searching for solutions of singular boundary value problems in the phase plane or in the three‐dimensional phase space. In this paper necesary and sufficient conditions are derived which are to be satisfied by the model parameters and the propagation velocity of the wave front if wave solutions exist. Moreover, sufficient conditions for the asymptotic stability of these solutions are proved where the perturbations are supposed to belong to a certain weightedL2‐space. Finally, the connection between the initial distribution of the state variable and the velocity of the wave is di

ISSN:0170-4214    

DOI:10.1002/mma.1670110504

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this article an existence theorem is proved for the coagulation–fragmentation equation with unbounded kernel rates. Solutions are shown to be in the spaceX+= {c∈L1: ∫ 0∞(1 +x)∣c(x)∣dx<∞} whenever the kernels satisfy certain growth properties and the non‐negative initial data belong toX+. The proof is based on weakL1compactness methods applied to suitably chosen approx

ISSN:0170-4214    

DOI:10.1002/mma.1670110505

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractSolutions of weakly non‐linear wave equations can be approximated using Galerkin's procedure combined with the averaging method. In this paper existence and uniqueness of solutions are proved in suitably chosen function spaces. Error‐estimates lead us to results on asymptotic validity of the approximations. Some applications are indica

ISSN:0170-4214    

DOI:10.1002/mma.1670110506

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractConsidernbounded domains Ω ⊆ ℝ k iand elliptic formally symmetric differential operatorsA1of second order on ΩiChoose any closed subspaceVin\documentclass{article}\pagestyle{empty}\begin{document}$ \prod\limits_{i = 1}^n {L^2 \left({\Omega _i } \right)} $\end{document}, and extend (Ai)i=1,…,nby Friedrich's theorem to a self‐adjoint operatorAwithD(A1/2) =V(interaction operator). We give asymptotic estimates for the eigenvalues ofAand consider wave equations with interaction.With this concept, we solve a large class of problems including interface problems and transmission problems on ramified spaces.25,32We also treat non‐linear interaction, using a the

ISSN:0170-4214    

DOI:10.1002/mma.1670110507

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY

摘要:

AbstractIn this paper we study a coupled non‐linear system of partial differential equations that models the dynamics of structural phase transitions in a one‐dimensional non‐viscous and heat‐conducting solid. The corresponding Helmholtz free energy density is assumed in Ginzburg–Landau form; to allow for phase transitions and hysteresis phenomena, it is not assumed convex in the order parameter. It is shown that the solution of the system depends continuously upon the data, and we prove an existence result for an associated optimal contro

ISSN:0170-4214    

DOI:10.1002/mma.1670110508

出版商:John Wiley&Sons, Ltd    

年代:1989

数据来源: WILEY