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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The N-periodic wave solutions of some coupled bilinear equations
耦合 双线性方程 N周期波解
2023/4/26
In this talk, we present an efficient numerical scheme to calculate the N-periodic wave solutions to the Tzitzeica equation, the (2+1)-dimensional modified Bogoyavlenskii-Schiff equation and the mKdV-...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Type II blowup solutions to the 5D semilinear heat equation with double power nonlinearity
双幂非线性 5D 双线性热方程 II型爆破解
2023/5/16
We will discuss the existence of blowup solutions to $u_t=\Delta u+|u|^\frac{4}{n-2}u-|u|^{q-1}u$ with $0inds of blowup solutions in this equation. I...
Electrified thin films:Global existence of non-negative solutions
Higher order equation Non-local equation Thin film equation Non-negative solutions
2015/10/15
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric...
Robust solutions to l1, l2, and l_infinity uncertain linear approximation problems using convex optimization
Linear random and uncertain data convex optimization
2015/8/11
We present minimax and stochastic formulations of some linear approximation problems with uncertain data in R^n equipped with the Euclidean (l2), Absolute-sum (l1) or Chebyshev (l-infinity) norms. We ...
Linear estimates for solutions of quadratic equations in free groups
Linear estimates solutions of quadratic equations Group Theory
2011/9/6
Abstract: We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by $2s$ for orientable equation and by $12s^4$ for no...
A polynomial bound on solutions of quadratic equations in free groups
polynomial bound quadratic equations free groups Group Theory
2011/8/31
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
Perturbational Blowup Solutions to the 2-Component Camassa-Holm Equations
Perturbational Blowup 2-Component Camassa-Holm Equations
2011/1/19
In this article, we study the perturbational method to construct the non-radially symmet-ric solutions of the compressible 2-component Camassa-Holm equations. In detail, we first combine the substitut...
Exact solutions for periodic and solitary matter waves in nonlinear lattices
Exact solutions periodic solitary matter waves nonlinear lattices
2010/12/28
We produce three vast classes of exact periodic and solitonic solutions to the one-dimensional
Gross-Pitaevskii equation (GPE) with the pseudopotential in the form of a nonlinear lattice (NL),induced...
Multiplicity and regularity of periodic solutions for a class of degenerate semilinear wave equations
Multiplicity regularity of periodic solutions class of degenerate semilinear wave equations
2011/2/28
We prove the existence of infinitely many classical periodic solutions for a class of degenerate semilinear wave equations:utt − uxx + |u|s−1u = f(x, t),for all s > 1. In particular we pro...
Large Deviations Principle by viscosity solutions: the case of diffusions with oblique Lipschitz reflections
Large Deviations Principle diffusions with oblique reflections
2011/1/21
We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control pro...
Uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations
nonlinear elliptic PDEs uniqueness of solutions quasiconformal mappings
2011/1/21
We settle the problem of the uniqueness of normalized homeomorphic solutions to nonlinear Beltrami equations @f(z) = H(z, @f(z)). It turns out that the uniqueness holds under definite and explicit bou...
Symmetry analysis and exact solutions of semilinear heat flow in multi-dimensions
Symmetry analysis exact solutions semilinear heat flow in multi-dimensions
2010/11/24
A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve...
Fock Spaces, Landau Operators and the Regular Solutions of time-harmonic Maxwell equations
Fock Spaces Landau Operators time-harmonic Maxwell equations
2010/11/24
We investigate the solution representation for Maxwell equations based on the combination of hypercomplex function-theoretical methods with quantum mechanical methods. This gives a characterization f...
Existence and concentration of solutions for a class of biharmonic equations
Existence and concentration of solutions biharmonic equations
2010/11/22
Some superlinear fourth order elliptic equations are considered. Ground states are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existe...
This article gives explicit solutions to the Yang-Mills equations. The solutions have positive energy that can be made arbitrarily small by selection of a parameter showing that Yang-Mills field theor...