Equivalence and new exact solutions to the Black Scholes and diffusion equations.
Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions...
Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle
Consider the problem of time-periodic strong solutions of the Stokes system modelling viscous incompressible fluid flow past a rotating obstacle in the whole space ℝ³. Introducing a rotating coordinate system attached to the body yields a system of partial differential equations of second order involving an angular derivative not subordinate to the Laplacian. In a recent paper [2] the author proved -estimates of second order derivatives uniformly in the angular and translational velocities, ω and...
Étude de l’équation où est une mesure positive
On montre que les solutions faibles de l’équation , où est une mesure positive négligeant les polaires, vérifient une inégalité de Harnack. On s’occupe également des sursolutions dont on fait la représentation intégrale a l’aide d’une fonction de Green. Comme les solutions sont discontinues, on est amené à utiliser les formules probabilistes.
Evolution operators for higher order abstract parabolic equations
Evolutionary equation of inertial waves in 3-D multiply connected domain with Dirichlet boundary condition.
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.
Exact controllability of a pluridimensional coupled problem.
We set a coupled boundary value problem between two domains of different dimension. The first one is the unit cube of Rn, n C [2,3], with a crack and the second one is the crack. this problem comes from Ciarlet et al. (1989), that obtained an analogous coupled problem. We show that the solution has singularities due to the crack. As in Grisvard (1989), we adapt the Hilbert uniqueness method of J.-L. Lions (1968,1988) in order to obtain the exact controllability of the associated wave equation with...
Exact solutions and localized structures for higher-dimensional Burgers systems.
Exact solutions for nonclassical Stefan problems.
Exact solutions of Cauchy problem for partial differential equations with double characteristics and singular coefficients
Exact Solutions of Nonlocal BVPs for the Multidimensional Heat Equations
MSC 2010: 44A35, 44A45, 44A40, 35K20, 35K05In this paper a method for obtaining exact solutions of the multidimensional heat equations with nonlocal boundary value conditions in a finite space domain with time-nonlocal initial condition is developed. One half of the space conditions are local, and the other are nonlocal. Extensions of Duhamel principle are obtained. In the case when the initial value condition is a local one i.e. of the form u(x1; :::; xn; 0) = f(x1; :::; xn) the problem reduces...
Exact Solutions of Nonlocal Pluriparabolic Problems
MSC 2010: 44A35, 44A40
Exact solutions of the generalized Benjamin-Bona-Mahony equation.
Exact solutions to KdV6 equation by using a new approach of the projective Riccati equation method.
Exact solutions to some nonlinear PDEs, travelling profiles method.
Example of solving of the boundary value problems for one partial differential equations with two unknown functions
Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. I.
Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II.
Existence and convergence of the expansion in the asymptotic theory of elastic thin plates