In this paper we study the time fractional semilinear diffusion equation 0 CD t α u (t, x)− Δ u
(t, x)=| u| p+ t σ w (x) with the initial conditions u (0, x)= u 0 (x) and∂ tu (0, x)= u 1 (x) for x∈ …

It is well known that inequalities are a very important tool in classical analysis. One
application of these inequalities is the theory of PDEs (Partial Differential Equations). To our …

We consider exterior boundary value problems with nontrivial boundary conditions,
including three types of semilinear equations: heat equation, wave equation and damped …

В предлагаемой книге излагается общий подход к априорным оценкам решений
нелинейных уравнений и неравенств в частных производных, основанный на методе …

We, first, consider the parabolic equationu t=−(− Δ) α/2u m+ a (x).∇ u q+ f (t, x)| u|'p+ w (t, x),
t> 0, x∈ RN, where (− Δ) α/2 is the α/2− fractional power of the Laplacian− Δ which for 0< …

In this paper, we use the Green's function method to get the pointwise convergence rate of
the semilinear pseudo-parabolic equations. By using this precise pointwise structure and …

We investigate the large-time behavior of the sign-changing solution of the inhomogeneous
semilinear heat equation∂ tu= Δ u+| u| p+ t σ w (x) in (0, T)× RN, where N≥ 2, p> 1, σ>− 1 …

The paper studies the large-time behavior of solutions to the Robin problem for PDEs with
critical nonlinearities. For the considered problems, nonexistence results are obtained …

In the present paper, we study an inhomogeneous pseudo-parabolic equation with nonlocal
nonlinearity ut− k Δ ut− Δ u= I 0+ γ (| u| p)+ ω (x),(t, x)∈(0,∞)× RN, where p> 1, k≥ 0, ω (x)≠ …

In this paper, we study a critical exponent to the semilinear heat equation with forcing term
on Heisenberg group. Our technique of proof is based on methods of nonlinear capacity …