Applied mathematics Higher order symmetries of the (2+1) heat equation with a source term UNIVERSITY OF CENTRAL ARKANSAS Daniel J. Arrigo ParhamZackSymmetry analysis has played an important role in obtaining exact solutions of partial differential equations. A particular class of equations that has ...
Blow-Up Rate Estimates and Liouville Type Theorems for a Semilinear Heat Equation with Weighted SourceSemilinear parabolic equation QH Phan - 《Theoretical & Experimental Plant Physiology》 被引量: 0发表: 2017年 Singularity and decay estimates in superlinear problems via Liouville-type theorems. Part ...
For the caseα=0, note that ifvsolves the initial value problem for the ordinary heat equation with initial valuea, then the function(t,x)↦etv(t,x)solves the initial value problem above. Hence, blow-up does not occur in this case. Intuitively, this can be explained by the fact that...
Most of the studies on static analysis of FGM were carried out either with [52,82] or without [70] considering the effect of internal heat source. Most of the two dimensional thermo-elastic studies were carried out using one dimensional heat conduction equation [41,83–86]. This is due ...
Gives better satisfaction of the continuity equation than Velocity-pressure formulation. Found to work best with standard fully connected networks. Also improves the accuracy of results in Fourier networks. SiReNs Applicable to all class of problems Shown to be effective for problems with sharp gradient...
Since the problem of the existence and nonexistence of solutions for (1.1) with A=1 can be reduced to the following equation (2.8) via the transformation (1.18) with A=1 under the condition (1.9), we here discuss the existence of solutions for the heat equation with the exponential nonline...
The Physics where The Heat Equation come from The structure of the heat solution Visualization decaying of the heat structure Building Symbolic heat structure Solving Heat Problem Separation of variables with BC Fourier Analysis of IC Embedding Fourier coefficients ...
7、n equation: u t 2u x2 = 0,0 x 1,t 0 u(x,0) = 100,0 x 1 u(0,t) x = h(0 u(0,t),t 0 u(1,t) x = h(0 u(1,t),t 0 with h convection heat-transfer coeffi cient, and thermal conductivity of the materia. And en general, h is much larger than , so to ...
The energy equation is formulated by taking into consideration both the heat absorption (or release) due to the phase change process and the conductivity enhancement induced by the motion of the particles. The heat source or heat generation function in the energy equation is derived from solutions...
They observed that the specific heat capacity of nanofluids having an EG-based fluid is lower than nanofluid with H2O as a base fluid. In addition, the coefficients in the equation of Vajjha and Das [11] were updated in order to obtain a new equation with a better prediction performance. ...