Andriy Kryvko

On the Ill-posed Hyperbolic Systems with a Multiplicity Change Point of Not Less Than the Third Order

Hyperbolic systems with noninvolutive multiple characteristics are considered and an example of ill-posed Cauchy problem is proposed.

Near shore seismic movements induced by seaquakes using the boundary element method

This study quantifies seismic amplifications in near-shore arising from seaquakes. Within the Boundary Element Method, boundary elements are used to irradiate waves and force densities obtained for each element. Huygens´ Principle is implemented since the diffracted waves are constructed at the boundary from which they are radiated, which is equivalent to Somigliana´s theorem. Application of boundary conditions leads to a system of integral equations of the Fredholm type of second kind and zero order. Several numerical configurations are analyzed: The first is used to verify the present formulation with ideal sea floor configurations to estimate seismic amplifications. With the formulation verified, simple slope configurations are studied to estimate spectra of seismic motions. It is found that P-waves can produce seismic amplifications from 1.2 to 3.9 times the amplitude of the incident wave. SV-waves can generate seismic amplifications up to 4.5 times the incident wave. Another relevant finding is that the highest amplifications are at the shore compared to the ones at the sea floor.

SEISMIC PRESSURES IN OFFSHORE AREAS: NUMERICAL RESULTS

THE PURPOSE OF THIS STUDY IS TO OBTAIN NUMERICAL ESTIMATIONS OF SEISMIC PRESSURES IN OFFSHORE AREAS CONSIDERING THE EFFECT OF SEABED CONFIGURATIONS AND MATERIALS. ACCORDING TO THE BOUNDARY ELEMENT METHOD, BOUNDARY ELEMENTS ARE USED TO IRRADIATE WAVES AND FORCE DENSITIES ARE DETERMINED. FROM THIS HYPOTHESIS, HUYGENS´ PRINCIPLE IS IMPLEMENTED SINCE THE DIFFRACTED WAVES ARE CONSTRUCTED AT THE BOUNDARY FROM WHICH THEY ARE RADIATED. APPLICATION OF BOUNDARY CONDITIONS ALLOWS US TO DETERMINE A SYSTEM OF INTEGRAL EQUATIONS OF FREDHOLM TYPE OF SECOND KIND. VARIOUS MODELS WERE ANALYZED, THE FIRST ONE IS USED TO VALIDATE THE PROPOSED FORMULATION. OTHER MODELS OF IDEAL SEABED CONFIGURATIONS ARE DEVELOPED TO ESTIMATE THE SEISMIC PRESSURE PROFILES AT SEVERAL LOCATIONS. THE INFLUENCE OF P- AND SV-WAVE INCIDENCE WAS ALSO HIGHLIGHTED. IN GENERAL TERMS, MATERIALS WITH HIGHER WAVE PROPAGATION VELOCITIES GENERATE A LESSER PRESSURE FIELD. THE DIFFERENCE BETWEEN THE MAXIMUM PRESSURE VALUES OBTAINED FOR A MATERIAL WITH SHEAR WAVE VELOCITY OF I²=3000 M/S IS APPROXIMATELY 9 TIMES LOWER THAN THOSE OBTAINED FOR A MATERIAL WITH I²=90 M/S, FOR THE P WAVE INCIDENCE, AND 2.5 TIMES FOR THE CASE OF SV WAVES. THESE RESULTS ARE RELEVANT BECAUSE THE SEABED MATERIAL HAS DIRECT IMPLICATIONS ON THE PRESSURE FIELD OBTAINED.

Justification of the asymptotic solutions of linear system with a turning point of high order

In the present paper justification of the asymptotic solutions of linear system with a high-order turning point constructed is proved.

Quantization conditions for the vector Sturm-Liouville problem

where y ∈ Cn;h ∈ (0, 1] is a small parameter. The matrix Sturm-Liouville problem occurs in quantum mechanics [1, 2] and in the nanotechnology [3, 4, 5]. Let A(x) = A(x)∗ be an (n×n) matrix function of class C∞(R1) such that operator (1) is essentially selfadjoint in L2(R) [6]. Denote the eigenvalues of the selfadjoint matrix A(x) by λj(x), j = 1, . . . , n. Let ej(x) be the orthonormalized eigenvectors of A(x), i.e., A(x)ej(x) = λj(x)ej(x). If the selfadjoint matrix A(x) is an analytic function on an open set V⊆ R1, then all eigenvalues and eigenvectors of the matrix are analytic functions on V [7]. Thus, we can assume that the following conditions hold.