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In the present paper we describe a method for solving inverse problems for the Helmholtz equation in radially-symmetric domains given multi-frequency data. Our approach is based on the construction of suitable trace formulas which relate…
We investigate problems related with the existence of square integrable holomorphic functions on (unbounded) balanced domains. In particular, we solve the problem of Wiegerinck for balanced domains in dimension two. We also give a…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
CFTs are naturally defined on Riemann surfaces. The rational ones can be solved using methods from algebraic geometry. One particular feature is the covariance of the partition function under the mapping class group. In genus $g=1$, this…
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This study introduces a recursive method for computing asymptotic solutions of the Laplace equation in corner domains with the homogeneous Dirichlet boundary condition on one side and the Robin boundary condition with a power-law…
This manuscript presents an efficient boundary integral equation technique for solving two-dimensional Helmholtz problems defined in the half-plane bounded by an infinite, periodic curve with Neumann boundary conditions and an aperiodic…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We characterize the set of positive harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of several different chambers. We analyze the asymptotic behavior of the solutions in connection with the changes…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…
Quasilinear systems with piecewise constant arguments of generalized type are under investigation from the asymptotic point of view. The systems have discontinuous right-hand sides which are identified via a discrete-time map. It is…
Integration operational matrix methods based on Zernike polynomials are used to determine approximate solutions of a class of non-homogeneous partial differential equations (PDEs) of first and second order. Due to the nature of the Zernike…
We review our algebraic framework for linear boundary problems (concentrating on ordinary differential equations). Its starting point is an appropriate algebraization of the domain of functions, which we have named integro-differential…
Using the theory of fixed point index, we establish new results for the existence of nonzero solutions of Hammerstein integral equations with reflections. We apply our results to a first order periodic boundary value problem with…
A numerical scheme is presented for solving the Helmholtz equation with Dirichlet or Neumann boundary conditions on piecewise smooth open curves, where the curves may have corners and multiple junctions. Existing integral equation methods…
This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…
We study the problem of the existence and the holomorphicity of the Monge-Amp\`ere foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Amp\`ere equation even at points of arbitrary degeneracy. We obtain…
In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and…