Results 51 to 60 of about 6,239,552 (226)
The exterior Dirichlet problem for the Helmholtz equation
Journal of Mathematical Analysis and Applications, 1975 AbstractThe exterior Dirichlet problem for the reduced wave equation is reformulated as a new integral equation. It is shown that the normal derivative of the total field may be expressed as a Neumann series in terms of the known incident field. The convergence of the infinite series is established for arbitrary smooth surfaces and for small values of ...
openaire +1 more source
Planar Coulomb Gas on a Jordan Arc at Any Temperature
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT We study a planar Coulomb gas confined to a sufficiently smooth Jordan arc γ$\gamma$ in the complex plane, at inverse temperature β>0$\beta > 0$. Let Z¯nβ(γ)=Znβ(γ)((2cap(γ))βn2/2e(1−β/2)n(H(νe,γ)−H(νe,I)),$$\begin{equation*} \bar{Z}_{n}^\beta (\gamma)=\frac{Z_n^\beta (\gamma)}{((2\text{cap}(\gamma))^{\beta n^2/2}e^{(1-\beta /2)n(H(\nu _{e ...
K. Courteaut, K. Johansson, F. Viklund
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Irrigation and Drainage, EarlyView.ABSTRACT Crop modelling is essential for agricultural water management but often relies on simplified water balance routines that limit representation of soil moisture dynamics. To address this limitation, we developed a coupled model that integrates the 1‐D Richards equation, solved using a finite difference method into the FAO AquaCrop.
Krishna Panthi +2 more
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International Journal of Mathematics and Mathematical Sciences, 2012 We study the Dirichlet problem for the 2D Laplace equation in a domain bounded by smooth closed curves and smooth cracks. In the formulation of the problem, we do not require compatibility conditions for Dirichlet's boundary data at the tips of the ...
P. A. Krutitskii
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The Dirichlet Problem for Lévy-stable operators with $L^2$-data
, 2023 Grube F, Hensiek T, Schefer W. The Dirichlet Problem for Lévy-stable operators with $L^2$-data. Calculus of Variations and Partial Differential Equations .
Schefer, Waldemar ; https://orcid.org/ +2 more
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An All‐At‐Once Solver for Visco‐Acoustic Full Waveform Inversion in the Time‐Domain
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT Full waveform inversion (FWI) is the cutting‐edge seismic imaging technique used to reconstruct subsurface material properties such as wave velocities, mass density, and attenuation from measurements of reflected wavefields. In this article, we present the first implementation of FWI in the visco‐acoustic regime, based on a new time‐domain all‐
Christian Rheinbay, Andreas Rieder
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A Phase‐Field Model for Quasi‐Dynamic Rupture Nucleation and Propagation of In‐Plane Faults
International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT Computational modeling of faulting processes is an essential tool for understanding earthquake mechanics but remains challenging due to the structural and material complexities of fault zones. The phase‐field method has recently enabled unified modeling of fault propagation and off‐fault damage within a fracture‐mechanics‐based framework ...
Fan Fei +3 more
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International Journal for Numerical and Analytical Methods in Geomechanics, EarlyView.ABSTRACT Swelling of clay‐sulfate rocks is a concern in geotechnical engineering that can damage infrastructure. In the historic town of Staufen in southwest Germany, geothermal drilling into a swellable anhydrite‐bearing clay formation resulted in water inflow and subsequent swelling, triggering ground heave and damage to more than 250 houses.
Reza Mahmoudi Kouhi +4 more
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Existence and uniqueness of solutions to Hardy-Henon boundary-value problems
Electronic Journal of Differential EquationsWe consider the elliptic equation $$ -\Delta u=d(x)^\alpha u^p,\quad x\in \Omega\quad (\text{or } x\in\mathbb{R}^N\setminus \overline{\Omega}), $$ where $\alpha, p \in \mathbb{R}$, $d(x) = \text{dist} (x,\partial\Omega)$ and $\Omega\subset\mathbb{R}^N$ $
Xiyou Cheng +3 more
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Parabolic problems with dynamical boundary conditions in perforated media
Mathematical Modelling and Analysis, 2003 The asymptotic behavior of the solution of a parabolic dynamical boundary‐value problem in a periodically perforated domain is analyzed. The perforations, which are identical and periodically distributed, are of size ϵ.
C. Timofte
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