Fujita blow-up solutions for a Dirichlet problem of parabolic equations with variable coefficients

Critical exponent of non‐global solutions for an inhomogeneous pseudo‐parabolic equation with space‐time forcing term

“…that is, when 1 < p < p c and ∫ R n 𝜔(x)dx > 0, (1.7) has no global solutions, while global solutions exist for suitably small u 0 and 𝜔 belonging to certain Lebesgue spaces when p ≥ p c . We refer to [29,38,39] about the critical exponent of non-global solutions to systems of heat equations with space-time forcing term. Recently, Zhou [47] investigated the Cauchy problem of the following inhomogeneous pseudo-parabolic equation:…”

“…$$ that is, when $$$ 1&lt;p&lt;{p}_c $$$ and $$$ {\int}_{{\mathrm{\mathbb{R}}}&#x0005E;n}\omega (x) dx&gt;0 $$$, () has no global solutions, while global solutions exist for suitably small $$$ {u}_0 $$$ and $$$ \omega $$$ belonging to certain Lebesgue spaces when $$$ p\ge {p}_c $$$. We refer to [29, 38, 39] about the critical exponent of non‐global solutions to systems of heat equations with space‐time forcing term.…”