Fundamental solution of the operator for n>3
Fundamental solution for operators preserving a quadratic form
Fundamental solutions of the differential operator
Fundamentallösungen von homogenen Differentialoperatoren [Book]
Generalized Gevrey classes and multi-quasi-hyperbolic operators.
Global analytic and Gevrey surjectivity of the Mizohata operator
The surjectivity of the operator from the Gevrey space , , onto itself and its non-surjectivity from to is proved.
Hausdorffovy míry a odstranitelné singularity parciálních diferenciálních rovnic
Heat kernels for class 2 nilpotent groups
Incompressible inviscid limit for the full magnetohydrodynamic flows on expanding domains
In this paper we study the incompressible inviscid limit of the full magnetohydrodynamic flows on expanding domains with general initial data. By applying the relative energy method and carrying out detailed analysis on the oscillation part of the velocity, we prove rigorously that the gradient part of the weak solutions of the full magnetohydrodynamic flows converges to the strong solution of the incompressible Euler system in the whole space, as the Mach number, viscosity as well as the heat conductivity...
Inhomogeneous Gevrey ultradistributions and Cauchy problem
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.
Invariant Eigendistributions on the Tangent Space of a Rank One Semisimple Symmetrie Space.
Invertibility of some second order differential operators
Kolmogorov Diameters in Solution Spaces of Systems of Partial Differential Equations.
Konstruktion von Fundamentallösungen für Convolutoren.
--Time decay estimate for solution of the Cauchy problem for hyperbolic partial differential equations of linear thermoelasticity
We prove the --time decay estimates for the solution of the Cauchy problem for the hyperbolic system of partial differential equations of linear thermoelasticity. In our proof based on the matrix of fundamental solutions to the system we use Strauss-Klainerman’s approach [12], [5] to the --time decay estimates.
-oценки решения задачи Коши для одномерного гиперболического уравнения высокого порядка с постоянными коэффициентами
Large time behaviour of solutions to nonhomogeneous diffusion equations
This note is devoted to the study of the long time behaviour of solutions to the heat and the porous medium equations in the presence of an external source term, using entropy methods and self-similar variables. Intermediate asymptotics and convergence results are shown using interpolation inequalities, Gagliardo-Nirenberg-Sobolev inequalities and Csiszár-Kullback type estimates.
Laurent series expansion for solutions of hypoelliptic equations
We prove that any zero solution of a hypoelliptic partial differential operator can be expanded in a generalized Laurent series near a point singularity if and only if the operator is semielliptic. Moreover, the coefficients may be calculated by means of a Cauchy integral type formula. In particular, we obtain explicit expansions for the solutions of the heat equation near a point singularity. To prove the necessity of semiellipticity, we additionally assume that the index of hypoellipticity with...