# Registered Data

Contents

- 1 [CT048]
- 1.1 [01587] Existence and multiplicity solutions for a fourth-order Neumann problem
- 1.2 [01524] Radon measure solutions to compressible Euler equations and applications
- 1.3 [02136] Nonlocal Boundary Value Problems with Local Boundary Conditions
- 1.4 [00251] Separable Variable Method and Exact Solution of Fractional Differential Equations
- 1.5 [00614] Sparse spectral methods for fractional PDEs

# [CT048]

## [01587] Existence and multiplicity solutions for a fourth-order Neumann problem

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Our aim is to study the existence, uniqueness and multiplicity results for weak solvability of the following fourth-order problem involving Leray-Lions type operator with the Neumann boundary conditions in variable exponent spaces $$ \Delta (a(x, \Delta u)) +b(x)|u|^{p(x)-2} u=\lambda f(x, u) \text { for } x \in \Omega, $$ with $$a(x, \Delta u) \cdot \nu(x)=\mu g(x, u) \text { for } x \in \partial \Omega.$$**Classification**:__35R03__,__35A15__,__35J40__**Author(s)**:**Said Taarabti**(university of Ibn Zohr)

## [01524] Radon measure solutions to compressible Euler equations and applications

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We proposed a definition of Radon measure solutions to the compressible Euler equations with general constitutive relations. With this definition, we proved the Newton-Busemann law for stationary hypersonic flow passing bodies, constructed delta shock solutions to the Riemann problems of the rectilinear barotropic Euler equations, justified the interpretation of delta shocks as free pistons. This shows the possibility of treating solid-fluid interaction problems by simpler Cauchy problems with solutions in the class of Radon measures.**Classification**:__35R06__,__35Q31__,__35D99__**Author(s)**:**Hairong Yuan**(East China Normal University )- Aifang Qu (Shanghai Normal University )

## [02136] Nonlocal Boundary Value Problems with Local Boundary Conditions

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We state and analyze classical boundary value problems for nonlocal operators. The model takes its horizon parameter to be spatially dependent, vanishing near the boundary of the domain. We show the variational convergence of solutions to the nonlocal problem with mollified Poisson data to the solution of the localized classical Poisson problem with $H^{-1}$ data as the horizon uniformly converges to zero. Several classes of boundary conditions are considered.**Classification**:__35R09__,__35J05__,__46E35__**Author(s)**:**James Scott**(Columbia University)- James M. Scott (Columbia University)

## [00251] Separable Variable Method and Exact Solution of Fractional Differential Equations

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: We demonstrate how the method of separation of variables provides an effective tool to derive exact solution of nonlinear time fractional PDEs as well as partial differential-difference equations. More specifically, exact solutions to discrete time fractional K-dV equation, time fractional Toda - lattice equation, time fractional heat equation and nonlinear time fractional telegraph equation with variable coefficients have been derived. The question of deriving exact solution satisfying initial and boundary conditions is also addressed.**Classification**:__35R11__,__34A08__**Author(s)**:**Ramajayam Sahadevan**(Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai-600005 )

## [00614] Sparse spectral methods for fractional PDEs

**Session Date & Time**: 4E (Aug.24, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Fractional partial differential equations model nonlocal processes such as wave absorption in the brain, long-range geophysical effects, and Lévy flights. We introduce a spectral method for the fractional Laplacian in one dimension that induces sparse linear systems. We only deal with the coefficients of the expansion and thus time-stepping is fast. We consider a number of examples including the fractional heat and fractional wave propagation equations.**Classification**:__35R11__,__65N35__,__65M70__,__65R10__,__Numerical Analysis, Nonlocal PDEs__**Author(s)**:**Ioannis P. A. Papadopoulos**(Imperial College London)