Data from the World Health Organization indicate that Bulgaria has second-highest COVID-19 mortality rate in world and lowest vaccination European Union. In this context, to find crucial epidemiological parameters characterize ongoing pandemic Bulgaria, we introduce an extended SEIRS model with time-dependent coefficients. addition this, vital dynamics are included model. We construct appropriate Cauchy problem for a system of nonlinear ordinary differential equations prove its unique...

We study a boundary value problem for (3 + 1)-D weakly hyperbolic equations of Keldysh type (problem PK). The Keldysh-type are known in some specific applications plasma physics, optics, and analysis on projective spaces. Problem PK is not well-posed since it has infinite-dimensional cokernel. Actually, this analogous to similar one proposed by M. Protter 1952, but Tricomi-type which, part, closely connected with transonic fluid dynamics. consider properly defined, special function space,...

Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Svetozar Margenov, Nedyu Popivanov, Iva Ugrinova, Stanislav Harizanov, Tsvetan Hristov; Mathematical computer modeling of COVID-19 transmission dynamics in Bulgaria by time-depended inverse SEIR model. AIP Conf. Proc. 8 March 2021; 2333 (1): 090024. https://doi.org/10.1063/5.0041868 Download citation file: Ris...

A $(3+1)$ -dimensional boundary value problem for equations of Keldysh type (the second kind) is studied. Such problems Tricomi first or the wave equation were formulated by M.H. Protter (1954) as multidimensional analogues Darboux Cauchy-Goursat plane problems. Now, it well known that are not correctly set, and they have singular generalized solutions, even smooth right-hand sides. In this paper an analogue given. An appropriate solution with possible singularity defined. Results uniqueness...

We consider the steady transonic small disturbance equations on a domain and with data that lead to solution depends single variable. After writing down solution, we show it can also be found by using hodograph transformation followed partial Fourier transform. This motivates considering perturbed problems solved same technique. identify class of such problems.

Views Icon Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Twitter Facebook Reddit LinkedIn Tools Reprints and Permissions Cite Search Site Citation Aleksey Nikolov, Nedyu Popivanov; Singular solutions to Protter's problem for (3+1)-D degenerate wave equation. AIP Conference Proceedings 1 November 2012; 1497 (1): 233–238. https://doi.org/10.1063/1.4766790 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote...

For the four-dimensional nonhomogeneous wave equation boundary value problems that are multidimensional analogues of Darboux in plane studied. It is known for smooth right-hand side functions unique generalized solution may have a strong power-type singularity at only one point. This isolated vertex<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>O</mml:mi></mml:mrow></mml:math>of light characteristic cone and does not propagate along bicharacteristics. The...

Some three-dimensional boundary value problems for mixed type equations of second kind are studied. Such problems, but first stated by M. Protter in the fifties. For hyperbolic-elliptic they multidimensional analogue classical two-dimensional Morawetz-Guderley transonic problem. hyperbolic and weakly 3D analogues Darboux or Cauchy-Goursat plane problems. In this case, contrast well-posedness 2D new strongly ill-posed. paper given similar statement Keldish type, involving lower order terms....

Some three-dimensional boundary value problems for equations of Keldysh type are studied. Such problems, but Tricomi stated by M. H. Protter [25] as 3-D analogues Darboux or Cauchy-Goursat plane problems. It is well known that in contrast well-posedness 2D the strongly ill-posed. In [12] problem formulated and it shown not correctly set since homogeneous adjoint has infinitely many nontrivial classical solutions. present paper a notion generalized solution to introduced. Further, results...

A three dimensional boundary value problem for equations of Keldysh type involving lower order terms is studied. This not correctly set, since it has an infinite-dimensional co-kernel. In to avoid the infinite number necessary conditions classical solvability a notion generalized solution given. For small power degeneration m ∈ (0, 1) results existence and uniqueness such are obtained, without supposing any vanishing on parabolic part first terms. result corresponds with so called Protter...

For the wave equation we study boundary value problems, which are four-dimensional analogues of Darboux problems on plane. It is shown that for n in ℕ there exists a right hand side smooth function from C , corresponding unique generalized solution has strong power-type singularity at point O. This isolated vertex O characteristic cone and does not propagate along cone. The present article describes exact behavior singular solutions We give some necessary sufficient conditions existence with...

In 1952, for the wave equation,Protter formulated some boundary value problems (BVPs), which are multidimensional analogues of Darboux on plane. He studied these in a 3D domain Ω 0 , bounded by two characteristic cones Σ 1 and 2,0 plane region . What is situation around BVPs now after 50 years? It well known that, infinite number smooth functions right‐hand side equation, do not have classical solutions. Popivanov Schneider (1995) discovered reason this fact cases Dirichlet′s or Neumann′s...

For nonlinear equations of Gellerstedt type, uniqueness generalized solutions to the degenerate hyperbolic Cauchy-Goursat problem on characteristic triangles will be established. homogeneous supercritical nonlinearities, trivial solution in class approved by combining suitable Pohožaev-type identities with well tailored mollifying procedures. The question what constitutes critical growth for clarified and differences mixed elliptic-hyperbolic type exhibited

Bulgaria has the lowest COVID-19 vaccination rate in European Union and second-highest mortality world. That is why we think it important better to understand reason for this situation analyse development of disease over time. In paper, an extended time-dependent SEIRS model SEIRS-VB used investigate long-term behaviour epidemic. This includes vital dynamics. To apply some numerical simulation tools have been developed a family time-discrete variants are introduced. Suitable inverse problems...