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Nonlinear damped wave equations for the sub-Laplacian on the Heisenberg group and for Rockland operators on graded Lie groups
In this paper we study the Cauchy problem for the semilinear damped wave equation for the sub-Laplacian on the Heisenberg group. In the case of the positive mass, we show the global in timeExpand
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Wave propagation with irregular dissipation and applications to acoustic problems and shallow waters
In this paper we consider an acoustic problem of wave propagation through a discontinuous medium. The problem is reduced to the dissipative wave equation with distributional dissipation. We show thatExpand
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Wave equation with distributional propagation speed and mass term : numerical simulations
In this paper we explore numerically the theoretical results of the paper [10], and report on the numerical study of the Cauchy-Dirichlet problem for the 1D wave equation with distributionalExpand
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Nonharmonic Analysis of Boundary Value Problems
In this paper, we develop the global symbolic calculus of pseudo-differential operators generated by a boundary value problem for a given (not necessarily self-adjoint or elliptic) differentialExpand
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Schatten classes, nuclearity and nonharmonic analysis on compact manifolds with boundary
Given a compact manifold $M$ with boundary $\partial M$, in this paper we introduce a global symbolic calculus of pseudo-differential operators associated to $(M,\partial M)$. The symbols ofExpand
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On regularized trace formulas for a well-posed perturbation of the m-Laplace operator
A class of well-posed problems in a Hilbert space for the m-Laplace operator in a punctured domain is considered. An analog of the Green formula and a class of self-adjoint problems are obtained. WeExpand
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Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For suchExpand
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Wave Equation for Operators with Discrete Spectrum and Irregular Propagation Speed
Given a Hilbert space $${\mathcal{H}}$$H, we investigate the well-posedness of the Cauchy problem for the wave equation for operators with a discrete non-negative spectrum acting onExpand
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WELL-POSED PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH INTEGRAL BOUNDARY CONDITIONS
In this remark we study the boundary-value problems for a fractional analogue of the Laplace equation with integral boundary conditions in rectangular and half-strip domains. We prove the existenceExpand
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On a non–local problem for a multi–term fractional diffusion-wave equation
Abstract This paper deals with the multi-term generalisation of the time-fractional diffusion-wave equation for general operators with discrete spectrum, as well as for positive hypoellipticExpand
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