Error Analysis for Laplace Transform - Finite Element Solution of Hyperbolic Equations
Error estimates of a numerical method for a class of nonlinear evolution equations
Existence and regularity of solutions of some elliptic system in domains with edges [Book]
First-order systems of linear partial differential equations: normal forms, canonical systems, transform methods
In this paper we consider first-order systems with constant coefficients for two real-valued functions of two real variables. This is both a problem in itself, as well as an alternative view of the classical linear partial differential equations of second order with constant coefficients. The classification of the systems is done using elementary methods of linear algebra. Each type presents its special canonical form in the associated characteristic coordinate system. Then you can formulate initial...
Fourier transform, oscillatory multipliers and evolution equations in rearrangement invariant function spaces
Global existence of solutions for a strongly coupled population system
A strongly coupled cross-diffusion model for two competing species in a heterogeneous environment is analyzed. We sketch the proof of an existence result for the evolution problem with non-flux boundary conditions in one space dimension, completing previous results [4]. The proof is based on a symmetrization of the problem via an exponential transformation of variables and the use of an entropy functional.
High Frequency limit of the Helmholtz Equations
We derive the high frequency limit of the Helmholtz equations in terms of quadratic observables. We prove that it can be written as a stationary Liouville equation with source terms. Our method is based on the Wigner Transform, which is a classical tool for evolution dispersive equations. We extend its use to the stationary case after an appropriate scaling of the Helmholtz equation. Several specific difficulties arise here; first, the identification of the source term (which does not share the...
Hypoelliptic operators with characteristic variety of codimension two and the wave equation
Injectivity of the spherical mean operator on the conical manifolds of spheres.
Integral transforms for divisors in and solutions of systems of PDE’s
Integral Transforms Method to Solve a Time-Space Fractional Diffusion Equation
Mathematical Subject Classification 2010: 35R11, 42A38, 26A33, 33E12.The method of integral transforms based on using a fractional generalization of the Fourier transform and the classical Laplace transform is applied for solving Cauchy-type problem for the time-space fractional diffusion equation expressed in terms of the Caputo time-fractional derivative and a generalized Riemann-Liouville space-fractional derivative.
Interpolation problems in cones. Nota I
In questa nota, si studiano problemi di interpolazione per varietà discrete in spazi di funzioni olomorfe in coni. In particolare si mostra come sia possibile estendere il Principio Fondamentale di Ehrenpreis ad equazioni di convoluzione nella spazio , introdotto in [4] in connessione con problemi di fisica quantistica.
Interpolation problems in cones. Nota II
Si estendono qui i risultati della nota precedente al caso di varietà non discrete. Ciò viene utilizzato per ottenere un teorema di rappresentazione per soluzioni di sistemi di equazioni di convoluzione in spazi di funzioni olomorfe in coni.
Inversion de la transformation de Pompeiu locale
Lamb's plane problem in a thermoelastic micropolar medium with stretch.
Laplace integrals in partial differential equations in papers of Bogdan Ziemian
Fundamental solutions to linear partial differential equations with constant coefficients are represented in the form of Laplace type integrals.
Laplace transform pairs of N-dimensions and second order linear partial differential equations with constant coefficients.
Lie Groups and KdV Equations.
Littlewood-paley decomposition associated with the dunkl operators and paraproduct operators.
New exact solutions for a reaction-diffusion equation and a quasi-Camassa Holm equation.