A priori estimate for discontinuous solutions of a second order linear hyperbolic problem.
Blow-up of solutions for a system of nonlinear wave equations with nonlinear damping.
Existence and boundary stabilization of the semilinear Mindlin-Timoshenko system.
Existence of solutions for hyperbolic system of second order outside a domain.
Explicit integration of equations of motion solved on computer cluster
In the last decade the dramatic onset of multicore and multi-processor systems in combination with the possibilities which now provide modern computer networks have risen. The complexity and size of the investigated models are constantly increasing due to the high computational complexity of computational tasks in dynamics and statics of structures, mainly because of the nonlinear character of the solved models. Any possibility to speed up such calculation procedures is more than desirable. This...
Global existence and energy decay of solutions to a Bresse system with delay terms
We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.
Global solutions of quasilinear systems of Klein–Gordon equations in 3D
We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.
Initial-boundary value problems for second order systems of partial differential equations
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must be satisfied by the solution of the larger first order...
Initial-boundary value problems for second order systems of partial differential equations∗
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of n equations as a larger first order system. Unfortunately, the resulting first order system consists, in general, of more than 2n equations which leads to many complications, such as side conditions which must...
Nonlinear boundary dissipation for a coupled system of Klein-Gordon equations.
Quasilineare Differentialgleichungen zweiter Ordnung vom hyperbolischen Typus. Gemischte Randwertaufgaben