Related papers: Group Classification of a generalization of the He…
A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new…
The present paper solves the problem of the group classification of the general Burgers' equation $u_t=f(x,u)u_x^2+g(x,u)u_{xx}$, where $f$ and $g$ are arbitrary smooth functions of the variable $x$ and $u$, by using Lie method. The paper…
An exhaustive group classification of variable coefficient generalized Kawahara equations is carried out. As a result, we derive new variable coefficient nonlinear models admitting Lie symmetry extensions. All inequivalent Lie reductions of…
We look at the semigroup generated by a system of heat equations. Applications to testing normality and option pricing are addressed.
In this work, we study the global well-posedeness of the heat equation with variable time-dependent nonlinearity of the form $\varphi(t)f(u)$ on unimodular Lie groups when the differential operator arises as the sum of squares of…
We present a generalization of Lie's method for finding the group invariant solutions to a system of partial differential equations. Our generalization relaxes the standard transversality assumption and encompasses the common situation…
Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms…
A class of inverse problems for a heat equation with involution perturbation is considered using four different boundary conditions, namely, Dirichlet, Neumann, periodic and anti-periodic boundary conditions. Proved theorems on existence…
In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations with functional derivatives. In order to perform the group analysis and deal with the functional…
The quantization of gauge fields and gravitation on manifolds with boundary makes it necessary to study boundary conditions which involve both normal and tangential derivatives of the quantized field. The resulting one-loop divergences can…
We present the hyperasymptotic expansions for a certain group of solutions of the heat equation. We extend this result to a more general case of linear PDEs with constant coefficients. The generalisation is based on the method of Borel…
In this paper we present a comparison principle for higher order nonlinear hypoelliptic heat operators on graded Lie groups. Moreover, using the comparison principle we obtain blow-up type results and global in $t$-boundedness of solutions…
Preliminary group classification for a class of generalized inviscid Burger's equations in the general form $u_t+g(x, u)u_x = f(x, u)$ is given and additional equivalence transformations are found. Adduced results complete and essentially…
In this article we consider a mathematical model of an initial stage of closure electrical contact that involves a metallic vaporization after instantaneous exploding of contact due to arc ignition with power $P_0$ on fixed face $z=0$ and…
In this letter we present the set of invariant difference equations and meshes which preserve the Lie group symmetries of the equation u_{t}=(K(u)u_{x})_{x}+Q(u). All special cases of K(u) and Q(u) that extend the symmetry group admitted by…
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general…
The analytic method for deriving the equation of state of a cell fluid model in the region above the critical temperature ($T \geqslant T_\text{c}$) is elaborated using the renormalization group transformation in the collective variables…
We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…
The group classification of a class of semilinear reaction-diffusion equations with exponential nonlinearity is carried out using the technique of mapping between classes, which was recently proposed in [O.O. Vaneeva, R.O. Popovych and C.…
We consider the heat equation defined by a generalized measure theoretic Laplacian on $[0,1]$. This equation describes heat diffusion in a bar such that the mass distribution of the bar is given by a non-atomic Borel probabiliy measure…