Without incorporation of weak-shock theory, the lossless Burgers equation predicts a multivalued waveform for nonlinear propagation beyond a certain distance. Inclusion of thermoviscous attenuation, which increases quadratically with frequency, prevents the occurrence of multivalued waveforms. The same is true for any attenuation law that is proportional to frequency raised to an exponent great...

where F : [0, 1]×R → P(R) is a compact valued multivalued map, P(R) is the family of all subsets of R, k ∈ (0, π 2 ), 0 < t1 < t2 < . . . < tm < 1, Ik ∈ C(R,R) (k = 1, 2, . . . , m), ∆x|t=tk = x(t + k )− x(t − k ), x(t + k ) and x(t − k ) represent the right and left limits of x(t) at t = tk respectively, k = 1, 2, . . . , m. In the literature there are few papers dealing with the existence of ...

In this paper, a new wavelet representation for multivalued images is presented. The idea for this representation is based on the first fundamental form that provides a local measure for the contrast of a multivalued image. In this paper, this concept is extended toward multiscale fundamental forms using the dyadic wavelet transform of Mallat. The multiscale fundamental forms provide a local me...

Recently‎, some researchers have established some results on existence of endpoints for multivalued mappings. In particular, Mohammadi and Rezapour's [Endpoints of Suzuki type quasi-contractive multifunctions, U.P.B. Sci. Bull., Series A, 2015] used the technique of $alpha-psi$-contractive mappings, due to Samet et al. (2012), to give some results about endpoints of Suzuki type quasi-contractiv...

In this work a model for planning with multivalued fluents and graded actions, based on the infinite valued Lukasiewicz logic, is introduced. In multivalued planning, fluents can assume truth values in the interval [0, 1] and actions can be executed at different application degrees also varying in [0, 1]. The notions of planning problem and solution plan also reflect a multivalued approach. Mul...

The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the ...

This is the second paper of a series of three on the regularity of higher codimension area minimizing integral currents. Here we perform the second main step in the analysis of the singularities, namely the construction of a center manifold, i.e. an approximate average of the sheets of an almost flat area minimizing current. Such a center manifold is accompanied by a Lipschitz multivalued map o...

Pseudomonotone∗ maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity∗ of the map implies the “maximum principle suff...

In this paper we study the optimal control of system driven by hemivariational inequality of second order. First, we establish the existence of solutions to hemivariational inequality which contains nonlinear pseudomonotone evolution operator. Introducing a control variable in the multivalued term of the generalized subdifferential, we prove the closedness (in suitable topologies) of the graph ...